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/******************************************************* |
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* |
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* Copyright (c) 2003-2008 by University of Queensland |
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* Earth Systems Science Computational Center (ESSCC) |
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* http://www.uq.edu.au/esscc |
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* |
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* Primary Business: Queensland, Australia |
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* Licensed under the Open Software License version 3.0 |
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* http://www.opensource.org/licenses/osl-3.0.php |
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* |
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*******************************************************/ |
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|
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|
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/**************************************************************/ |
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|
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/* Finley: */ |
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|
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/**************************************************************/ |
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|
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#include "Quadrature.h" |
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|
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#define QUADNODES(_K_,_I_) quadNodes[INDEX2(_K_,_I_,DIM)] |
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#define QUADWEIGHTS(_I_) quadWeights[_I_] |
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|
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/**************************************************************/ |
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|
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/* get a quadrature scheme with numQuadNodes quadrature nodes for the tri */ |
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/* as a queezed scheme on a quad [0,1]^2 */ |
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|
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void Finley_Quad_getNodesTri(int numQuadNodes,double* quadNodes,double* quadWeights) { |
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int i; |
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double Q1,Q2,a,b,c,d,e,f,g,u,v,w; |
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#define DIM 2 |
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|
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/* the easy cases: */ |
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|
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if (numQuadNodes==1) { |
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QUADNODES(0,0)=1./3.; |
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QUADNODES(1,0)=1./3.; |
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QUADWEIGHTS(0)=1./2.; |
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} else if (numQuadNodes==3){ |
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QUADNODES(0,0)=1./2.; |
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QUADNODES(1,0)=0.; |
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QUADWEIGHTS(0)=1./6.; |
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QUADNODES(0,1)=0.; |
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QUADNODES(1,1)=1./2.; |
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QUADWEIGHTS(1)=1./6.; |
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QUADNODES(0,2)=1./2.; |
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QUADNODES(1,2)=1./2.; |
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QUADWEIGHTS(2)=1./6.; |
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} else if (numQuadNodes==4){ |
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QUADNODES(0,0)=1./3.; |
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QUADNODES(1,0)=1./3.; |
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QUADWEIGHTS(0)=-27./96.; |
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QUADNODES(0,1)=0.2; |
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QUADNODES(1,1)=0.2; |
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QUADWEIGHTS(1)=25./96.; |
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QUADNODES(0,2)=0.6; |
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QUADNODES(1,2)=0.2; |
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QUADWEIGHTS(2)=25./96.; |
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QUADNODES(0,3)=0.2; |
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QUADNODES(1,3)=0.6; |
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QUADWEIGHTS(3)=25./96.; |
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} else if (numQuadNodes==6){ |
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QUADWEIGHTS(0) = 0.109951743655322/2.; |
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QUADWEIGHTS(1) = 0.109951743655322/2.; |
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QUADWEIGHTS(2) = 0.109951743655322/2.; |
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QUADWEIGHTS(3) = 0.223381589678011/2.; |
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QUADWEIGHTS(4) = 0.223381589678011/2.; |
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QUADWEIGHTS(5) = 0.223381589678011/2.; |
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|
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QUADNODES(0,0) = 0.816847572980459; |
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QUADNODES(0,1) = 0.091576213509771; |
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QUADNODES(0,2) = 0.091576213509771; |
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QUADNODES(0,3) = 0.108103018168070; |
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QUADNODES(0,4) = 0.445948490915965; |
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QUADNODES(0,5) = 0.445948490915965; |
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|
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QUADNODES(1,0) = 0.091576213509771; |
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QUADNODES(1,1) = 0.816847572980459; |
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QUADNODES(1,2) = 0.091576213509771; |
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QUADNODES(1,3) = 0.445948490915965; |
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QUADNODES(1,4) = 0.108103018168070; |
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QUADNODES(1,5) = 0.445948490915965; |
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|
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} else if (numQuadNodes==7){ |
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QUADNODES(0,0) = 0.33333333333333333; |
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QUADNODES(0,1) = 0.7974269853530872; |
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QUADNODES(0,2) = 0.10128650732345633; |
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QUADNODES(0,3) = 0.10128650732345633; |
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QUADNODES(0,4) = 0.059715871789769809; |
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QUADNODES(0,5) = 0.47014206410511505; |
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QUADNODES(0,6) = 0.47014206410511505; |
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|
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QUADNODES(1,0) = 0.33333333333333333; |
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QUADNODES(1,1) = 0.10128650732345633; |
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QUADNODES(1,2) = 0.7974269853530872; |
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QUADNODES(1,3) = 0.10128650732345633; |
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QUADNODES(1,4) = 0.47014206410511505; |
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QUADNODES(1,5) = 0.059715871789769809; |
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QUADNODES(1,6) = 0.47014206410511505; |
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|
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QUADWEIGHTS(0) = 0.225/2.; |
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QUADWEIGHTS(1) = 0.12593918054482717/2.; |
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QUADWEIGHTS(2) = 0.12593918054482717/2.; |
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QUADWEIGHTS(3) = 0.12593918054482717/2.; |
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QUADWEIGHTS(4) = 0.13239415278850616/2.; |
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QUADWEIGHTS(5) = 0.13239415278850616/2.; |
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QUADWEIGHTS(6) = 0.13239415278850616/2.; |
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|
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} else if (numQuadNodes==12){ |
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a = 0.873821971016996; |
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b = 0.063089014491502; |
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c = 0.501426509658179; |
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d = 0.249286745170910; |
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e = 0.636502499121399; |
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f = 0.310352451033785; |
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g = 0.053145049844816; |
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|
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u = 0.050844906370207/2.; |
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v = 0.116786275726379/2.; |
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w = 0.082851075618374/2.; |
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|
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QUADNODES(0,0) = a; |
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QUADNODES(0,1) = b; |
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QUADNODES(0,2) = b; |
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QUADNODES(0,3) = c; |
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QUADNODES(0,4) = d; |
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QUADNODES(0,5) = d; |
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QUADNODES(0,6) = e; |
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QUADNODES(0,7) = e; |
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QUADNODES(0,8) = f; |
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QUADNODES(0,9) = f; |
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QUADNODES(0,10) = g; |
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QUADNODES(0,11) = g; |
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|
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QUADNODES(1,0) = b; |
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QUADNODES(1,1) = a; |
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QUADNODES(1,2) = b; |
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QUADNODES(1,3) = d; |
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QUADNODES(1,4) = c; |
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QUADNODES(1,5) = d; |
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QUADNODES(1,6) = f; |
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QUADNODES(1,7) = g; |
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QUADNODES(1,8) = e; |
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QUADNODES(1,9) = g; |
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QUADNODES(1,10) = e; |
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QUADNODES(1,11) = f; |
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|
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QUADWEIGHTS(0)= u; |
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QUADWEIGHTS(1)= u; |
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QUADWEIGHTS(2)= u; |
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QUADWEIGHTS(3)= v; |
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QUADWEIGHTS(4)= v; |
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QUADWEIGHTS(5)= v; |
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QUADWEIGHTS(6)= w; |
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QUADWEIGHTS(7)= w; |
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QUADWEIGHTS(8)= w; |
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QUADWEIGHTS(9)= w; |
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QUADWEIGHTS(10)= w; |
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QUADWEIGHTS(11)= w; |
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|
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} else if (numQuadNodes==13){ |
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QUADWEIGHTS(0) =-0.149570044467670/2.; |
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QUADWEIGHTS(1) = 0.175615257433204/2.; |
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QUADWEIGHTS(2) = 0.175615257433204/2.; |
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QUADWEIGHTS(3) = 0.175615257433204/2.; |
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QUADWEIGHTS(4) = 0.053347235608839/2.; |
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QUADWEIGHTS(5) = 0.053347235608839/2.; |
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QUADWEIGHTS(6) = 0.053347235608839/2.; |
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QUADWEIGHTS(7) = 0.077113760890257/2.; |
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QUADWEIGHTS(8) = 0.077113760890257/2.; |
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QUADWEIGHTS(9) = 0.077113760890257/2.; |
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QUADWEIGHTS(10) = 0.077113760890257/2.; |
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QUADWEIGHTS(11) = 0.077113760890257/2.; |
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QUADWEIGHTS(12) = 0.077113760890257/2.; |
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|
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QUADNODES(0,0) = 0.3333333333333333; |
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QUADNODES(0,1) = 0.479308067841923; |
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QUADNODES(0,2) = 0.260345966079038; |
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QUADNODES(0,3) = 0.260345966079038; |
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QUADNODES(0,4) = 0.869739794195568; |
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QUADNODES(0,5) = 0.065130102902216; |
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QUADNODES(0,6) = 0.065130102902216; |
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QUADNODES(0,7) = 0.638444188569809; |
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QUADNODES(0,8) = 0.638444188569809; |
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QUADNODES(0,9) = 0.048690315425316; |
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QUADNODES(0,10) = 0.048690315425316; |
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QUADNODES(0,11) = 0.312865496004875; |
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QUADNODES(0,12) = 0.312865496004875; |
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|
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QUADNODES(1,0) = 0.3333333333333333; |
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QUADNODES(1,1) = 0.260345966079038; |
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QUADNODES(1,2) = 0.479308067841923; |
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QUADNODES(1,3) = 0.260345966079038; |
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QUADNODES(1,4) = 0.065130102902216; |
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QUADNODES(1,5) = 0.869739794195568; |
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QUADNODES(1,6) = 0.065130102902216; |
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QUADNODES(1,7) = 0.048690315425316; |
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QUADNODES(1,8) = 0.312865496004875; |
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QUADNODES(1,9) = 0.638444188569809; |
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QUADNODES(1,10) = 0.312865496004875; |
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QUADNODES(1,11) = 0.638444188569809; |
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QUADNODES(1,12) = 0.048690315425316; |
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|
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} else if (numQuadNodes==16){ |
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QUADWEIGHTS(0) = 0.07215780; |
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QUADWEIGHTS(1) = 0.04754582; |
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QUADWEIGHTS(2) = 0.04754582; |
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QUADWEIGHTS(3) = 0.04754582; |
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QUADWEIGHTS(4) = 0.01622925; |
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QUADWEIGHTS(5) = 0.01622925; |
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QUADWEIGHTS(6) = 0.01622925; |
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QUADWEIGHTS(7) = 0.05160869; |
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QUADWEIGHTS(8) = 0.05160869; |
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QUADWEIGHTS(9) = 0.05160869; |
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QUADWEIGHTS(10) = 0.01361516; |
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QUADWEIGHTS(11) = 0.01361516; |
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QUADWEIGHTS(12) = 0.01361516; |
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QUADWEIGHTS(13) = 0.01361516; |
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QUADWEIGHTS(14) = 0.01361516; |
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QUADWEIGHTS(15) = 0.01361516; |
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|
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QUADNODES(0,0) = 0.3333333; |
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QUADNODES(0,1) = 0.08141482; |
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QUADNODES(0,2) = 0.4592926; |
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QUADNODES(0,3) = 0.4592926; |
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QUADNODES(0,4) = 0.8989055; |
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QUADNODES(0,5) = 0.05054723; |
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QUADNODES(0,6) = 0.05054723; |
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QUADNODES(0,7) = 0.6588614; |
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QUADNODES(0,8) = 0.1705693; |
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QUADNODES(0,9) = 0.1705693; |
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QUADNODES(0,10) = 0.008394777; |
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QUADNODES(0,11) = 0.008394777; |
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QUADNODES(0,12) = 0.7284924; |
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QUADNODES(0,13) = 0.7284924; |
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QUADNODES(0,14) = 0.2631128; |
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QUADNODES(0,15) = 0.2631128; |
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|
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QUADNODES(1,0) = 0.3333333; |
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QUADNODES(1,1) = 0.4592926; |
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QUADNODES(1,2) = 0.08141482; |
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QUADNODES(1,3) = 0.4592926; |
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QUADNODES(1,4) = 0.05054723; |
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QUADNODES(1,5) = 0.8989055; |
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QUADNODES(1,6) = 0.05054723; |
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QUADNODES(1,7) = 0.1705693; |
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QUADNODES(1,8) = 0.6588614; |
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QUADNODES(1,9) = 0.1705693; |
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QUADNODES(1,10) = 0.7284924; |
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QUADNODES(1,11) = 0.2631128; |
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QUADNODES(1,12) = 0.008394777; |
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QUADNODES(1,13) = 0.2631128; |
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QUADNODES(1,14) = 0.008394777; |
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QUADNODES(1,15) = 0.7284924; |
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|
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} else if (numQuadNodes==19){ |
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QUADWEIGHTS(0) = 0.04856790; |
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QUADWEIGHTS(1) = 0.01566735; |
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QUADWEIGHTS(2) = 0.01566735; |
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QUADWEIGHTS(3) = 0.01566735; |
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QUADWEIGHTS(4) = 0.03891377; |
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QUADWEIGHTS(5) = 0.03891377; |
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QUADWEIGHTS(6) = 0.03891377; |
| 267 |
QUADWEIGHTS(7) = 0.03982387; |
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QUADWEIGHTS(8) = 0.03982387; |
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QUADWEIGHTS(9) = 0.03982387; |
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QUADWEIGHTS(10) = 0.01278884; |
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QUADWEIGHTS(11) = 0.01278884; |
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QUADWEIGHTS(12) = 0.01278884; |
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QUADWEIGHTS(13) = 0.02164177; |
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QUADWEIGHTS(14) = 0.02164177; |
| 275 |
QUADWEIGHTS(15) = 0.02164177; |
| 276 |
QUADWEIGHTS(16) = 0.02164177; |
| 277 |
QUADWEIGHTS(17) = 0.02164177; |
| 278 |
QUADWEIGHTS(18) = 0.02164177; |
| 279 |
|
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QUADNODES(0,0) = 0.3333333; |
| 281 |
QUADNODES(0,1) = 0.02063496; |
| 282 |
QUADNODES(0,2) = 0.4896825; |
| 283 |
QUADNODES(0,3) = 0.4896825; |
| 284 |
QUADNODES(0,4) = 0.1258208; |
| 285 |
QUADNODES(0,5) = 0.4370896; |
| 286 |
QUADNODES(0,6) = 0.4370896; |
| 287 |
QUADNODES(0,7) = 0.6235929; |
| 288 |
QUADNODES(0,8) = 0.1882035; |
| 289 |
QUADNODES(0,9) = 0.1882035; |
| 290 |
QUADNODES(0,10) = 0.9105410; |
| 291 |
QUADNODES(0,11) = 0.04472951; |
| 292 |
QUADNODES(0,12) = 0.04472951; |
| 293 |
QUADNODES(0,13) = 0.03683841; |
| 294 |
QUADNODES(0,14) = 0.03683841; |
| 295 |
QUADNODES(0,15) = 0.7411986; |
| 296 |
QUADNODES(0,16) = 0.7411986; |
| 297 |
QUADNODES(0,17) = 0.2219630; |
| 298 |
QUADNODES(0,18) = 0.2219630; |
| 299 |
|
| 300 |
QUADNODES(1,0) = 0.3333333; |
| 301 |
QUADNODES(1,1) = 0.4896825; |
| 302 |
QUADNODES(1,2) = 0.02063496; |
| 303 |
QUADNODES(1,3) = 0.4896825; |
| 304 |
QUADNODES(1,4) = 0.4370896; |
| 305 |
QUADNODES(1,5) = 0.1258208; |
| 306 |
QUADNODES(1,6) = 0.4370896; |
| 307 |
QUADNODES(1,7) = 0.1882035; |
| 308 |
QUADNODES(1,8) = 0.6235929; |
| 309 |
QUADNODES(1,9) = 0.1882035; |
| 310 |
QUADNODES(1,10) = 0.04472951; |
| 311 |
QUADNODES(1,11) = 0.9105410; |
| 312 |
QUADNODES(1,12) = 0.04472951; |
| 313 |
QUADNODES(1,13) = 0.7411986; |
| 314 |
QUADNODES(1,14) = 0.2219630; |
| 315 |
QUADNODES(1,15) = 0.03683841; |
| 316 |
QUADNODES(1,16) = 0.2219630; |
| 317 |
QUADNODES(1,17) = 0.03683841; |
| 318 |
QUADNODES(1,18) = 0.7411986; |
| 319 |
} else { |
| 320 |
|
| 321 |
/* get scheme on [0.1]^2 */ |
| 322 |
Finley_Quad_getNodesRec(numQuadNodes,quadNodes,quadWeights); |
| 323 |
if (! Finley_noError()) return; |
| 324 |
|
| 325 |
/* squeeze it: */ |
| 326 |
|
| 327 |
for (i=0;i<numQuadNodes;i++) { |
| 328 |
Q1=QUADNODES(0,i); |
| 329 |
Q2=QUADNODES(1,i); |
| 330 |
QUADWEIGHTS(i)=QUADWEIGHTS(i)*(1.-(1./2.)*(Q1+Q2)); |
| 331 |
QUADNODES(0,i)=Q1*(1.-(1./2.)*Q2); |
| 332 |
QUADNODES(1,i)=Q2*(1.-(1./2.)*Q1); |
| 333 |
} |
| 334 |
} |
| 335 |
#undef DIM |
| 336 |
|
| 337 |
|
| 338 |
} |
| 339 |
|
| 340 |
/**************************************************************/ |
| 341 |
|
| 342 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for the tet */ |
| 343 |
/* as a queezed scheme on a hex [0,1]^3 */ |
| 344 |
|
| 345 |
void Finley_Quad_getNodesTet(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 346 |
int i; |
| 347 |
double Q1,Q2,Q3,JA11,JA12,JA13,JA21,JA22,JA23,JA31,JA32,JA33,DET; |
| 348 |
double a,b,c,d,e,f,g,h; |
| 349 |
double alpha=0.58541019662496852; |
| 350 |
double beta =0.1381966011250105; |
| 351 |
#define DIM 3 |
| 352 |
|
| 353 |
/* the easy cases: */ |
| 354 |
if (numQuadNodes==1) { |
| 355 |
QUADNODES(0,0)=0.25; |
| 356 |
QUADNODES(1,0)=0.25; |
| 357 |
QUADNODES(2,0)=0.25; |
| 358 |
QUADWEIGHTS(0)=1./6.; |
| 359 |
} else if (numQuadNodes==4){ |
| 360 |
QUADNODES(0,0)=beta; |
| 361 |
QUADNODES(1,0)=beta; |
| 362 |
QUADNODES(2,0)=beta; |
| 363 |
QUADWEIGHTS(0)=1./24.; |
| 364 |
QUADNODES(0,1)=alpha; |
| 365 |
QUADNODES(1,1)=beta; |
| 366 |
QUADNODES(2,1)=beta; |
| 367 |
QUADWEIGHTS(1)=1./24.; |
| 368 |
QUADNODES(0,2)=beta; |
| 369 |
QUADNODES(1,2)=alpha; |
| 370 |
QUADNODES(2,2)=beta; |
| 371 |
QUADWEIGHTS(2)=1./24.; |
| 372 |
QUADNODES(0,3)=beta; |
| 373 |
QUADNODES(1,3)=beta; |
| 374 |
QUADNODES(2,3)=alpha; |
| 375 |
QUADWEIGHTS(3)=1./24.; |
| 376 |
} else if (numQuadNodes==5){ |
| 377 |
QUADNODES(0,0)=1./4.; |
| 378 |
QUADNODES(1,0)=1./4.; |
| 379 |
QUADNODES(2,0)=1./4.; |
| 380 |
QUADWEIGHTS(0)=-2./15.; |
| 381 |
QUADNODES(0,1)=1./6.; |
| 382 |
QUADNODES(1,1)=1./6.; |
| 383 |
QUADNODES(2,1)=1./6.; |
| 384 |
QUADWEIGHTS(1)=3./40.; |
| 385 |
QUADNODES(0,2)=1./2.; |
| 386 |
QUADNODES(1,2)=1./6.; |
| 387 |
QUADNODES(2,2)=1./6.; |
| 388 |
QUADWEIGHTS(2)=3./40.; |
| 389 |
QUADNODES(0,3)=1./6.; |
| 390 |
QUADNODES(1,3)=1./2.; |
| 391 |
QUADNODES(2,3)=1./6.; |
| 392 |
QUADWEIGHTS(3)=3./40.; |
| 393 |
QUADNODES(0,4)=1./6.; |
| 394 |
QUADNODES(1,4)=1./6.; |
| 395 |
QUADNODES(2,4)=1./2.; |
| 396 |
QUADWEIGHTS(4)=3./40.; |
| 397 |
|
| 398 |
} else if (numQuadNodes==11){ |
| 399 |
|
| 400 |
a = 0.25; |
| 401 |
b = 11.0/14.0; |
| 402 |
c = 1.0/14.0; |
| 403 |
d = 0.25 * (1.0 + sqrt ( 5.0 / 14.0 ) ); |
| 404 |
e = 0.25 * (1.0 - sqrt ( 5.0 / 14.0 ) ); |
| 405 |
f = -74.0 / 5625.0; |
| 406 |
g = 343.0 / 45000.0; |
| 407 |
h = 56.0 / 2250.0; |
| 408 |
|
| 409 |
QUADWEIGHTS(401-401) = f; |
| 410 |
QUADWEIGHTS(402-401) = g; |
| 411 |
QUADWEIGHTS(403-401) = g; |
| 412 |
QUADWEIGHTS(404-401) = g; |
| 413 |
QUADWEIGHTS(405-401) = g; |
| 414 |
QUADWEIGHTS(406-401) = h; |
| 415 |
QUADWEIGHTS(407-401) = h; |
| 416 |
QUADWEIGHTS(408-401) = h; |
| 417 |
QUADWEIGHTS(409-401) = h; |
| 418 |
QUADWEIGHTS(410-401) = h; |
| 419 |
QUADWEIGHTS(411-401) = h; |
| 420 |
|
| 421 |
QUADNODES(0,401-401) = a; |
| 422 |
QUADNODES(0,402-401) = b; |
| 423 |
QUADNODES(0,403-401) = c; |
| 424 |
QUADNODES(0,404-401) = c; |
| 425 |
QUADNODES(0,405-401) = c; |
| 426 |
QUADNODES(0,406-401) = d; |
| 427 |
QUADNODES(0,407-401) = d; |
| 428 |
QUADNODES(0,408-401) = d; |
| 429 |
QUADNODES(0,409-401) = e; |
| 430 |
QUADNODES(0,410-401) = e; |
| 431 |
QUADNODES(0,411-401) = e; |
| 432 |
|
| 433 |
QUADNODES(1,401-401) = a; |
| 434 |
QUADNODES(1,402-401) = c; |
| 435 |
QUADNODES(1,403-401) = b; |
| 436 |
QUADNODES(1,404-401) = c; |
| 437 |
QUADNODES(1,405-401) = c; |
| 438 |
QUADNODES(1,406-401) = d; |
| 439 |
QUADNODES(1,407-401) = e; |
| 440 |
QUADNODES(1,408-401) = e; |
| 441 |
QUADNODES(1,409-401) = d; |
| 442 |
QUADNODES(1,410-401) = d; |
| 443 |
QUADNODES(1,411-401) = e; |
| 444 |
|
| 445 |
QUADNODES(2,401-401) = a; |
| 446 |
QUADNODES(2,402-401) = c; |
| 447 |
QUADNODES(2,403-401) = c; |
| 448 |
QUADNODES(2,404-401) = b; |
| 449 |
QUADNODES(2,405-401) = c; |
| 450 |
QUADNODES(2,406-401) = e; |
| 451 |
QUADNODES(2,407-401) = d; |
| 452 |
QUADNODES(2,408-401) = e; |
| 453 |
QUADNODES(2,409-401) = d; |
| 454 |
QUADNODES(2,410-401) = e; |
| 455 |
QUADNODES(2,411-401) = d; |
| 456 |
|
| 457 |
} else if (numQuadNodes==15){ |
| 458 |
QUADWEIGHTS(412-412) = 0.019753086419753086; |
| 459 |
QUADWEIGHTS(413-412) = 0.01198951396316977; |
| 460 |
QUADWEIGHTS(414-412) = 0.01198951396316977; |
| 461 |
QUADWEIGHTS(415-412) = 0.01198951396316977; |
| 462 |
QUADWEIGHTS(416-412) = 0.01198951396316977; |
| 463 |
QUADWEIGHTS(417-412) = 0.011511367871045397; |
| 464 |
QUADWEIGHTS(418-412) = 0.011511367871045397; |
| 465 |
QUADWEIGHTS(419-412) = 0.011511367871045397; |
| 466 |
QUADWEIGHTS(420-412) = 0.011511367871045397; |
| 467 |
QUADWEIGHTS(421-412) = 0.0088183421516754845; |
| 468 |
QUADWEIGHTS(422-412) = 0.0088183421516754845; |
| 469 |
QUADWEIGHTS(423-412) = 0.0088183421516754845; |
| 470 |
QUADWEIGHTS(424-412) = 0.0088183421516754845; |
| 471 |
QUADWEIGHTS(425-412) = 0.0088183421516754845; |
| 472 |
QUADWEIGHTS(426-412) = 0.0088183421516754845; |
| 473 |
|
| 474 |
QUADNODES(0,412-412) = 0.2500000; |
| 475 |
QUADNODES(0,413-412) = 0.091971078052723032; |
| 476 |
QUADNODES(0,414-412) = 0.72408676584183096; |
| 477 |
QUADNODES(0,415-412) = 0.091971078052723032; |
| 478 |
QUADNODES(0,416-412) = 0.091971078052723032; |
| 479 |
QUADNODES(0,417-412) = 0.31979362782962989; |
| 480 |
QUADNODES(0,418-412) = 0.040619116511110234; |
| 481 |
QUADNODES(0,419-412) = 0.31979362782962989; |
| 482 |
QUADNODES(0,420-412) = 0.31979362782962989; |
| 483 |
QUADNODES(0,421-412) = 0.056350832689629149; |
| 484 |
QUADNODES(0,422-412) = 0.056350832689629149; |
| 485 |
QUADNODES(0,423-412) = 0.056350832689629149; |
| 486 |
QUADNODES(0,424-412) = 0.4436491673103708; |
| 487 |
QUADNODES(0,425-412) = 0.4436491673103708; |
| 488 |
QUADNODES(0,426-412) = 0.4436491673103708; |
| 489 |
|
| 490 |
QUADNODES(1,412-412) = 0.2500000; |
| 491 |
QUADNODES(1,413-412) = 0.091971078052723032; |
| 492 |
QUADNODES(1,414-412) = 0.091971078052723032; |
| 493 |
QUADNODES(1,415-412) = 0.72408676584183096; |
| 494 |
QUADNODES(1,416-412) = 0.091971078052723032; |
| 495 |
QUADNODES(1,417-412) = 0.31979362782962989; |
| 496 |
QUADNODES(1,418-412) = 0.31979362782962989; |
| 497 |
QUADNODES(1,419-412) = 0.040619116511110234; |
| 498 |
QUADNODES(1,420-412) = 0.31979362782962989; |
| 499 |
QUADNODES(1,421-412) = 0.056350832689629149; |
| 500 |
QUADNODES(1,422-412) = 0.4436491673103708; |
| 501 |
QUADNODES(1,423-412) = 0.4436491673103708; |
| 502 |
QUADNODES(1,424-412) = 0.056350832689629149; |
| 503 |
QUADNODES(1,425-412) = 0.056350832689629149; |
| 504 |
QUADNODES(1,426-412) = 0.4436491673103708; |
| 505 |
|
| 506 |
QUADNODES(2,412-412) = 0.2500000; |
| 507 |
QUADNODES(2,413-412) = 0.091971078052723032; |
| 508 |
QUADNODES(2,414-412) = 0.091971078052723032; |
| 509 |
QUADNODES(2,415-412) = 0.091971078052723032; |
| 510 |
QUADNODES(2,416-412) = 0.72408676584183096; |
| 511 |
QUADNODES(2,417-412) = 0.31979362782962989; |
| 512 |
QUADNODES(2,418-412) = 0.31979362782962989; |
| 513 |
QUADNODES(2,419-412) = 0.31979362782962989; |
| 514 |
QUADNODES(2,420-412) = 0.040619116511110234; |
| 515 |
QUADNODES(2,421-412) = 0.4436491673103708; |
| 516 |
QUADNODES(2,422-412) = 0.056350832689629149; |
| 517 |
QUADNODES(2,423-412) = 0.4436491673103708; |
| 518 |
QUADNODES(2,424-412) = 0.056350832689629149; |
| 519 |
QUADNODES(2,425-412) = 0.4436491673103708; |
| 520 |
QUADNODES(2,426-412) = 0.056350832689629149; |
| 521 |
|
| 522 |
} else if (numQuadNodes==24){ |
| 523 |
QUADWEIGHTS(427-427) = 0.006653792; |
| 524 |
QUADWEIGHTS(428-427) = 0.006653792; |
| 525 |
QUADWEIGHTS(429-427) = 0.006653792; |
| 526 |
QUADWEIGHTS(430-427) = 0.006653792; |
| 527 |
QUADWEIGHTS(431-427) = 0.001679535; |
| 528 |
QUADWEIGHTS(432-427) = 0.001679535; |
| 529 |
QUADWEIGHTS(433-427) = 0.001679535; |
| 530 |
QUADWEIGHTS(434-427) = 0.001679535; |
| 531 |
QUADWEIGHTS(435-427) = 0.009226197; |
| 532 |
QUADWEIGHTS(436-427) = 0.009226197; |
| 533 |
QUADWEIGHTS(437-427) = 0.009226197; |
| 534 |
QUADWEIGHTS(438-427) = 0.009226197; |
| 535 |
QUADWEIGHTS(439-427) = 0.008035714; |
| 536 |
QUADWEIGHTS(440-427) = 0.008035714; |
| 537 |
QUADWEIGHTS(441-427) = 0.008035714; |
| 538 |
QUADWEIGHTS(442-427) = 0.008035714; |
| 539 |
QUADWEIGHTS(443-427) = 0.008035714; |
| 540 |
QUADWEIGHTS(444-427) = 0.008035714; |
| 541 |
QUADWEIGHTS(445-427) = 0.008035714; |
| 542 |
QUADWEIGHTS(446-427) = 0.008035714; |
| 543 |
QUADWEIGHTS(447-427) = 0.008035714; |
| 544 |
QUADWEIGHTS(448-427) = 0.008035714; |
| 545 |
QUADWEIGHTS(449-427) = 0.008035714; |
| 546 |
QUADWEIGHTS(450-427) = 0.008035714; |
| 547 |
|
| 548 |
QUADNODES(0,427-427) = 0.3561914; |
| 549 |
QUADNODES(0,428-427) = 0.2146029; |
| 550 |
QUADNODES(0,429-427) = 0.2146029; |
| 551 |
QUADNODES(0,430-427) = 0.2146029; |
| 552 |
QUADNODES(0,431-427) = 0.8779781; |
| 553 |
QUADNODES(0,432-427) = 0.04067396; |
| 554 |
QUADNODES(0,433-427) = 0.04067396; |
| 555 |
QUADNODES(0,434-427) = 0.04067396; |
| 556 |
QUADNODES(0,435-427) = 0.03298633; |
| 557 |
QUADNODES(0,436-427) = 0.3223379; |
| 558 |
QUADNODES(0,437-427) = 0.3223379; |
| 559 |
QUADNODES(0,438-427) = 0.3223379; |
| 560 |
QUADNODES(0,439-427) = 0.6030057; |
| 561 |
QUADNODES(0,440-427) = 0.6030057; |
| 562 |
QUADNODES(0,441-427) = 0.6030057; |
| 563 |
QUADNODES(0,442-427) = 0.2696723; |
| 564 |
QUADNODES(0,443-427) = 0.2696723; |
| 565 |
QUADNODES(0,444-427) = 0.2696723; |
| 566 |
QUADNODES(0,445-427) = 0.06366100; |
| 567 |
QUADNODES(0,446-427) = 0.06366100; |
| 568 |
QUADNODES(0,447-427) = 0.06366100; |
| 569 |
QUADNODES(0,448-427) = 0.06366100; |
| 570 |
QUADNODES(0,449-427) = 0.06366100; |
| 571 |
QUADNODES(0,450-427) = 0.06366100; |
| 572 |
|
| 573 |
QUADNODES(1,427-427) = 0.2146029; |
| 574 |
QUADNODES(1,428-427) = 0.3561914; |
| 575 |
QUADNODES(1,429-427) = 0.2146029; |
| 576 |
QUADNODES(1,430-427) = 0.2146029; |
| 577 |
QUADNODES(1,431-427) = 0.04067396; |
| 578 |
QUADNODES(1,432-427) = 0.8779781; |
| 579 |
QUADNODES(1,433-427) = 0.04067396; |
| 580 |
QUADNODES(1,434-427) = 0.04067396; |
| 581 |
QUADNODES(1,435-427) = 0.3223379; |
| 582 |
QUADNODES(1,436-427) = 0.03298633; |
| 583 |
QUADNODES(1,437-427) = 0.3223379; |
| 584 |
QUADNODES(1,438-427) = 0.3223379; |
| 585 |
QUADNODES(1,439-427) = 0.2696723; |
| 586 |
QUADNODES(1,440-427) = 0.06366100; |
| 587 |
QUADNODES(1,441-427) = 0.06366100; |
| 588 |
QUADNODES(1,442-427) = 0.6030057; |
| 589 |
QUADNODES(1,443-427) = 0.06366100; |
| 590 |
QUADNODES(1,444-427) = 0.06366100; |
| 591 |
QUADNODES(1,445-427) = 0.6030057; |
| 592 |
QUADNODES(1,446-427) = 0.6030057; |
| 593 |
QUADNODES(1,447-427) = 0.2696723; |
| 594 |
QUADNODES(1,448-427) = 0.2696723; |
| 595 |
QUADNODES(1,449-427) = 0.06366100; |
| 596 |
QUADNODES(1,450-427) = 0.06366100; |
| 597 |
|
| 598 |
QUADNODES(2,427-427) = 0.2146029; |
| 599 |
QUADNODES(2,428-427) = 0.2146029; |
| 600 |
QUADNODES(2,429-427) = 0.3561914; |
| 601 |
QUADNODES(2,430-427) = 0.2146029; |
| 602 |
QUADNODES(2,431-427) = 0.04067396; |
| 603 |
QUADNODES(2,432-427) = 0.04067396; |
| 604 |
QUADNODES(2,433-427) = 0.8779781; |
| 605 |
QUADNODES(2,434-427) = 0.04067396; |
| 606 |
QUADNODES(2,435-427) = 0.3223379; |
| 607 |
QUADNODES(2,436-427) = 0.3223379; |
| 608 |
QUADNODES(2,437-427) = 0.03298633; |
| 609 |
QUADNODES(2,438-427) = 0.3223379; |
| 610 |
QUADNODES(2,439-427) = 0.06366100; |
| 611 |
QUADNODES(2,440-427) = 0.2696723; |
| 612 |
QUADNODES(2,441-427) = 0.06366100; |
| 613 |
QUADNODES(2,442-427) = 0.06366100; |
| 614 |
QUADNODES(2,443-427) = 0.6030057; |
| 615 |
QUADNODES(2,444-427) = 0.06366100; |
| 616 |
QUADNODES(2,445-427) = 0.2696723; |
| 617 |
QUADNODES(2,446-427) = 0.06366100; |
| 618 |
QUADNODES(2,447-427) = 0.6030057; |
| 619 |
QUADNODES(2,448-427) = 0.06366100; |
| 620 |
QUADNODES(2,449-427) = 0.6030057; |
| 621 |
QUADNODES(2,450-427) = 0.2696723; |
| 622 |
|
| 623 |
} else if (numQuadNodes==31){ |
| 624 |
QUADWEIGHTS(451-451) = 0.01826422; |
| 625 |
QUADWEIGHTS(452-451) = 0.01059994; |
| 626 |
QUADWEIGHTS(453-451) = 0.01059994; |
| 627 |
QUADWEIGHTS(454-451) = 0.01059994; |
| 628 |
QUADWEIGHTS(455-451) = 0.01059994; |
| 629 |
QUADWEIGHTS(456-451) =-0.06251774; |
| 630 |
QUADWEIGHTS(457-451) =-0.06251774; |
| 631 |
QUADWEIGHTS(458-451) =-0.06251774; |
| 632 |
QUADWEIGHTS(459-451) =-0.06251774; |
| 633 |
QUADWEIGHTS(460-451) = 0.004891425; |
| 634 |
QUADWEIGHTS(461-451) = 0.004891425; |
| 635 |
QUADWEIGHTS(462-451) = 0.004891425; |
| 636 |
QUADWEIGHTS(463-451) = 0.004891425; |
| 637 |
QUADWEIGHTS(464-451) = 0.0009700176; |
| 638 |
QUADWEIGHTS(465-451) = 0.0009700176; |
| 639 |
QUADWEIGHTS(466-451) = 0.0009700176; |
| 640 |
QUADWEIGHTS(467-451) = 0.0009700176; |
| 641 |
QUADWEIGHTS(468-451) = 0.0009700176; |
| 642 |
QUADWEIGHTS(469-451) = 0.0009700176; |
| 643 |
QUADWEIGHTS(470-451) = 0.02755732; |
| 644 |
QUADWEIGHTS(471-451) = 0.02755732; |
| 645 |
QUADWEIGHTS(472-451) = 0.02755732; |
| 646 |
QUADWEIGHTS(473-451) = 0.02755732; |
| 647 |
QUADWEIGHTS(474-451) = 0.02755732; |
| 648 |
QUADWEIGHTS(475-451) = 0.02755732; |
| 649 |
QUADWEIGHTS(476-451) = 0.02755732; |
| 650 |
QUADWEIGHTS(477-451) = 0.02755732; |
| 651 |
QUADWEIGHTS(478-451) = 0.02755732; |
| 652 |
QUADWEIGHTS(479-451) = 0.02755732; |
| 653 |
QUADWEIGHTS(480-451) = 0.02755732; |
| 654 |
QUADWEIGHTS(481-451) = 0.02755732; |
| 655 |
|
| 656 |
QUADNODES(0,451-451) = 0.2500000; |
| 657 |
QUADNODES(0,452-451) = 0.7653604; |
| 658 |
QUADNODES(0,453-451) = 0.07821319; |
| 659 |
QUADNODES(0,454-451) = 0.07821319; |
| 660 |
QUADNODES(0,455-451) = 0.07821319; |
| 661 |
QUADNODES(0,456-451) = 0.6344704; |
| 662 |
QUADNODES(0,457-451) = 0.1218432; |
| 663 |
QUADNODES(0,458-451) = 0.1218432; |
| 664 |
QUADNODES(0,459-451) = 0.1218432; |
| 665 |
QUADNODES(0,460-451) = 0.002382507; |
| 666 |
QUADNODES(0,461-451) = 0.3325392; |
| 667 |
QUADNODES(0,462-451) = 0.3325392; |
| 668 |
QUADNODES(0,463-451) = 0.3325392; |
| 669 |
QUADNODES(0,464-451) = 0.0000000; |
| 670 |
QUADNODES(0,465-451) = 0.0000000; |
| 671 |
QUADNODES(0,466-451) = 0.0000000; |
| 672 |
QUADNODES(0,467-451) = 0.5000000; |
| 673 |
QUADNODES(0,468-451) = 0.5000000; |
| 674 |
QUADNODES(0,469-451) = 0.5000000; |
| 675 |
QUADNODES(0,470-451) = 0.6000000; |
| 676 |
QUADNODES(0,471-451) = 0.6000000; |
| 677 |
QUADNODES(0,472-451) = 0.6000000; |
| 678 |
QUADNODES(0,473-451) = 0.2000000; |
| 679 |
QUADNODES(0,474-451) = 0.2000000; |
| 680 |
QUADNODES(0,475-451) = 0.2000000; |
| 681 |
QUADNODES(0,476-451) = 0.1000000; |
| 682 |
QUADNODES(0,477-451) = 0.1000000; |
| 683 |
QUADNODES(0,478-451) = 0.1000000; |
| 684 |
QUADNODES(0,479-451) = 0.1000000; |
| 685 |
QUADNODES(0,480-451) = 0.1000000; |
| 686 |
QUADNODES(0,481-451) = 0.1000000; |
| 687 |
|
| 688 |
QUADNODES(1,451-451) = 0.2500000; |
| 689 |
QUADNODES(1,452-451) = 0.07821319; |
| 690 |
QUADNODES(1,453-451) = 0.7653604; |
| 691 |
QUADNODES(1,454-451) = 0.07821319; |
| 692 |
QUADNODES(1,455-451) = 0.07821319; |
| 693 |
QUADNODES(1,456-451) = 0.1218432; |
| 694 |
QUADNODES(1,457-451) = 0.6344704; |
| 695 |
QUADNODES(1,458-451) = 0.1218432; |
| 696 |
QUADNODES(1,459-451) = 0.1218432; |
| 697 |
QUADNODES(1,460-451) = 0.3325392; |
| 698 |
QUADNODES(1,461-451) = 0.002382507; |
| 699 |
QUADNODES(1,462-451) = 0.3325392; |
| 700 |
QUADNODES(1,463-451) = 0.3325392; |
| 701 |
QUADNODES(1,464-451) = 0.0000000; |
| 702 |
QUADNODES(1,465-451) = 0.5000000; |
| 703 |
QUADNODES(1,466-451) = 0.5000000; |
| 704 |
QUADNODES(1,467-451) = 0.0000000; |
| 705 |
QUADNODES(1,468-451) = 0.0000000; |
| 706 |
QUADNODES(1,469-451) = 0.5000000; |
| 707 |
QUADNODES(1,470-451) = 0.2000000; |
| 708 |
QUADNODES(1,471-451) = 0.1000000; |
| 709 |
QUADNODES(1,472-451) = 0.1000000; |
| 710 |
QUADNODES(1,473-451) = 0.6000000; |
| 711 |
QUADNODES(1,474-451) = 0.1000000; |
| 712 |
QUADNODES(1,475-451) = 0.1000000; |
| 713 |
QUADNODES(1,476-451) = 0.6000000; |
| 714 |
QUADNODES(1,477-451) = 0.6000000; |
| 715 |
QUADNODES(1,478-451) = 0.2000000; |
| 716 |
QUADNODES(1,479-451) = 0.2000000; |
| 717 |
QUADNODES(1,480-451) = 0.1000000; |
| 718 |
QUADNODES(1,481-451) = 0.1000000; |
| 719 |
|
| 720 |
QUADNODES(2,451-451) = 0.2500000; |
| 721 |
QUADNODES(2,452-451) = 0.07821319; |
| 722 |
QUADNODES(2,453-451) = 0.07821319; |
| 723 |
QUADNODES(2,454-451) = 0.7653604; |
| 724 |
QUADNODES(2,455-451) = 0.07821319; |
| 725 |
QUADNODES(2,456-451) = 0.1218432; |
| 726 |
QUADNODES(2,457-451) = 0.1218432; |
| 727 |
QUADNODES(2,458-451) = 0.6344704; |
| 728 |
QUADNODES(2,459-451) = 0.1218432; |
| 729 |
QUADNODES(2,460-451) = 0.3325392; |
| 730 |
QUADNODES(2,461-451) = 0.3325392; |
| 731 |
QUADNODES(2,462-451) = 0.002382507; |
| 732 |
QUADNODES(2,463-451) = 0.3325392; |
| 733 |
QUADNODES(2,464-451) = 0.5000000; |
| 734 |
QUADNODES(2,465-451) = 0.0000000; |
| 735 |
QUADNODES(2,466-451) = 0.5000000; |
| 736 |
QUADNODES(2,467-451) = 0.0000000; |
| 737 |
QUADNODES(2,468-451) = 0.5000000; |
| 738 |
QUADNODES(2,469-451) = 0.0000000; |
| 739 |
QUADNODES(2,470-451) = 0.1000000; |
| 740 |
QUADNODES(2,471-451) = 0.2000000; |
| 741 |
QUADNODES(2,472-451) = 0.1000000; |
| 742 |
QUADNODES(2,473-451) = 0.1000000; |
| 743 |
QUADNODES(2,474-451) = 0.6000000; |
| 744 |
QUADNODES(2,475-451) = 0.1000000; |
| 745 |
QUADNODES(2,476-451) = 0.2000000; |
| 746 |
QUADNODES(2,477-451) = 0.1000000; |
| 747 |
QUADNODES(2,478-451) = 0.6000000; |
| 748 |
QUADNODES(2,479-451) = 0.1000000; |
| 749 |
QUADNODES(2,480-451) = 0.6000000; |
| 750 |
QUADNODES(2,481-451) = 0.2000000; |
| 751 |
|
| 752 |
} else if (numQuadNodes==45){ |
| 753 |
QUADWEIGHTS(482-482) =-0.03932701; |
| 754 |
QUADWEIGHTS(483-482) = 0.004081316; |
| 755 |
QUADWEIGHTS(484-482) = 0.004081316; |
| 756 |
QUADWEIGHTS(485-482) = 0.004081316; |
| 757 |
QUADWEIGHTS(486-482) = 0.004081316; |
| 758 |
QUADWEIGHTS(487-482) = 0.0006580868; |
| 759 |
QUADWEIGHTS(488-482) = 0.0006580868; |
| 760 |
QUADWEIGHTS(489-482) = 0.0006580868; |
| 761 |
QUADWEIGHTS(490-482) = 0.0006580868; |
| 762 |
QUADWEIGHTS(491-482) = 0.004384259; |
| 763 |
QUADWEIGHTS(492-482) = 0.004384259; |
| 764 |
QUADWEIGHTS(493-482) = 0.004384259; |
| 765 |
QUADWEIGHTS(494-482) = 0.004384259; |
| 766 |
QUADWEIGHTS(495-482) = 0.004384259; |
| 767 |
QUADWEIGHTS(496-482) = 0.004384259; |
| 768 |
QUADWEIGHTS(497-482) = 0.01383006; |
| 769 |
QUADWEIGHTS(498-482) = 0.01383006; |
| 770 |
QUADWEIGHTS(499-482) = 0.01383006; |
| 771 |
QUADWEIGHTS(500-482) = 0.01383006; |
| 772 |
QUADWEIGHTS(501-482) = 0.01383006; |
| 773 |
QUADWEIGHTS(502-482) = 0.01383006; |
| 774 |
QUADWEIGHTS(503-482) = 0.004240437; |
| 775 |
QUADWEIGHTS(504-482) = 0.004240437; |
| 776 |
QUADWEIGHTS(505-482) = 0.004240437; |
| 777 |
QUADWEIGHTS(506-482) = 0.004240437; |
| 778 |
QUADWEIGHTS(507-482) = 0.004240437; |
| 779 |
QUADWEIGHTS(508-482) = 0.004240437; |
| 780 |
QUADWEIGHTS(509-482) = 0.004240437; |
| 781 |
QUADWEIGHTS(510-482) = 0.004240437; |
| 782 |
QUADWEIGHTS(511-482) = 0.004240437; |
| 783 |
QUADWEIGHTS(512-482) = 0.004240437; |
| 784 |
QUADWEIGHTS(513-482) = 0.004240437; |
| 785 |
QUADWEIGHTS(514-482) = 0.004240437; |
| 786 |
QUADWEIGHTS(515-482) = 0.002238740; |
| 787 |
QUADWEIGHTS(516-482) = 0.002238740; |
| 788 |
QUADWEIGHTS(517-482) = 0.002238740; |
| 789 |
QUADWEIGHTS(518-482) = 0.002238740; |
| 790 |
QUADWEIGHTS(519-482) = 0.002238740; |
| 791 |
QUADWEIGHTS(520-482) = 0.002238740; |
| 792 |
QUADWEIGHTS(521-482) = 0.002238740; |
| 793 |
QUADWEIGHTS(522-482) = 0.002238740; |
| 794 |
QUADWEIGHTS(523-482) = 0.002238740; |
| 795 |
QUADWEIGHTS(524-482) = 0.002238740; |
| 796 |
QUADWEIGHTS(525-482) = 0.002238740; |
| 797 |
QUADWEIGHTS(526-482) = 0.002238740; |
| 798 |
|
| 799 |
QUADNODES(0,482-482) = 0.2500000; |
| 800 |
QUADNODES(0,483-482) = 0.6175872; |
| 801 |
QUADNODES(0,484-482) = 0.1274709; |
| 802 |
QUADNODES(0,485-482) = 0.1274709; |
| 803 |
QUADNODES(0,486-482) = 0.1274709; |
| 804 |
QUADNODES(0,487-482) = 0.9037635; |
| 805 |
QUADNODES(0,488-482) = 0.03207883; |
| 806 |
QUADNODES(0,489-482) = 0.03207883; |
| 807 |
QUADNODES(0,490-482) = 0.03207883; |
| 808 |
QUADNODES(0,491-482) = 0.4502229; |
| 809 |
QUADNODES(0,492-482) = 0.4502229; |
| 810 |
QUADNODES(0,493-482) = 0.4502229; |
| 811 |
QUADNODES(0,494-482) = 0.04977710; |
| 812 |
QUADNODES(0,495-482) = 0.04977710; |
| 813 |
QUADNODES(0,496-482) = 0.04977710; |
| 814 |
QUADNODES(0,497-482) = 0.3162696; |
| 815 |
QUADNODES(0,498-482) = 0.3162696; |
| 816 |
QUADNODES(0,499-482) = 0.3162696; |
| 817 |
QUADNODES(0,500-482) = 0.1837304; |
| 818 |
QUADNODES(0,501-482) = 0.1837304; |
| 819 |
QUADNODES(0,502-482) = 0.1837304; |
| 820 |
QUADNODES(0,503-482) = 0.5132800; |
| 821 |
QUADNODES(0,504-482) = 0.5132800; |
| 822 |
QUADNODES(0,505-482) = 0.5132800; |
| 823 |
QUADNODES(0,506-482) = 0.02291779; |
| 824 |
QUADNODES(0,507-482) = 0.02291779; |
| 825 |
QUADNODES(0,508-482) = 0.02291779; |
| 826 |
QUADNODES(0,509-482) = 0.2319011; |
| 827 |
QUADNODES(0,510-482) = 0.2319011; |
| 828 |
QUADNODES(0,511-482) = 0.2319011; |
| 829 |
QUADNODES(0,512-482) = 0.2319011; |
| 830 |
QUADNODES(0,513-482) = 0.2319011; |
| 831 |
QUADNODES(0,514-482) = 0.2319011; |
| 832 |
QUADNODES(0,515-482) = 0.1937465; |
| 833 |
QUADNODES(0,516-482) = 0.1937465; |
| 834 |
QUADNODES(0,517-482) = 0.1937465; |
| 835 |
QUADNODES(0,518-482) = 0.7303134; |
| 836 |
QUADNODES(0,519-482) = 0.7303134; |
| 837 |
QUADNODES(0,520-482) = 0.7303134; |
| 838 |
QUADNODES(0,521-482) = 0.03797005; |
| 839 |
QUADNODES(0,522-482) = 0.03797005; |
| 840 |
QUADNODES(0,523-482) = 0.03797005; |
| 841 |
QUADNODES(0,524-482) = 0.03797005; |
| 842 |
QUADNODES(0,525-482) = 0.03797005; |
| 843 |
QUADNODES(0,526-482) = 0.03797005; |
| 844 |
|
| 845 |
QUADNODES(1,482-482) = 0.2500000; |
| 846 |
QUADNODES(1,483-482) = 0.1274709; |
| 847 |
QUADNODES(1,484-482) = 0.6175872; |
| 848 |
QUADNODES(1,485-482) = 0.1274709; |
| 849 |
QUADNODES(1,486-482) = 0.1274709; |
| 850 |
QUADNODES(1,487-482) = 0.03207883; |
| 851 |
QUADNODES(1,488-482) = 0.9037635; |
| 852 |
QUADNODES(1,489-482) = 0.03207883; |
| 853 |
QUADNODES(1,490-482) = 0.03207883; |
| 854 |
QUADNODES(1,491-482) = 0.4502229; |
| 855 |
QUADNODES(1,492-482) = 0.04977710; |
| 856 |
QUADNODES(1,493-482) = 0.04977710; |
| 857 |
QUADNODES(1,494-482) = 0.4502229; |
| 858 |
QUADNODES(1,495-482) = 0.4502229; |
| 859 |
QUADNODES(1,496-482) = 0.04977710; |
| 860 |
QUADNODES(1,497-482) = 0.3162696; |
| 861 |
QUADNODES(1,498-482) = 0.1837304; |
| 862 |
QUADNODES(1,499-482) = 0.1837304; |
| 863 |
QUADNODES(1,500-482) = 0.3162696; |
| 864 |
QUADNODES(1,501-482) = 0.3162696; |
| 865 |
QUADNODES(1,502-482) = 0.1837304; |
| 866 |
QUADNODES(1,503-482) = 0.02291779; |
| 867 |
QUADNODES(1,504-482) = 0.2319011; |
| 868 |
QUADNODES(1,505-482) = 0.2319011; |
| 869 |
QUADNODES(1,506-482) = 0.5132800; |
| 870 |
QUADNODES(1,507-482) = 0.2319011; |
| 871 |
QUADNODES(1,508-482) = 0.2319011; |
| 872 |
QUADNODES(1,509-482) = 0.5132800; |
| 873 |
QUADNODES(1,510-482) = 0.5132800; |
| 874 |
QUADNODES(1,511-482) = 0.02291779; |
| 875 |
QUADNODES(1,512-482) = 0.02291779; |
| 876 |
QUADNODES(1,513-482) = 0.2319011; |
| 877 |
QUADNODES(1,514-482) = 0.2319011; |
| 878 |
QUADNODES(1,515-482) = 0.7303134; |
| 879 |
QUADNODES(1,516-482) = 0.03797005; |
| 880 |
QUADNODES(1,517-482) = 0.03797005; |
| 881 |
QUADNODES(1,518-482) = 0.1937465; |
| 882 |
QUADNODES(1,519-482) = 0.03797005; |
| 883 |
QUADNODES(1,520-482) = 0.03797005; |
| 884 |
QUADNODES(1,521-482) = 0.1937465; |
| 885 |
QUADNODES(1,522-482) = 0.1937465; |
| 886 |
QUADNODES(1,523-482) = 0.7303134; |
| 887 |
QUADNODES(1,524-482) = 0.7303134; |
| 888 |
QUADNODES(1,525-482) = 0.03797005; |
| 889 |
QUADNODES(1,526-482) = 0.03797005; |
| 890 |
|
| 891 |
QUADNODES(2,482-482) = 0.2500000; |
| 892 |
QUADNODES(2,483-482) = 0.1274709; |
| 893 |
QUADNODES(2,484-482) = 0.1274709; |
| 894 |
QUADNODES(2,485-482) = 0.6175872; |
| 895 |
QUADNODES(2,486-482) = 0.1274709; |
| 896 |
QUADNODES(2,487-482) = 0.03207883; |
| 897 |
QUADNODES(2,488-482) = 0.03207883; |
| 898 |
QUADNODES(2,489-482) = 0.9037635; |
| 899 |
QUADNODES(2,490-482) = 0.03207883; |
| 900 |
QUADNODES(2,491-482) = 0.04977710; |
| 901 |
QUADNODES(2,492-482) = 0.4502229; |
| 902 |
QUADNODES(2,493-482) = 0.04977710; |
| 903 |
QUADNODES(2,494-482) = 0.4502229; |
| 904 |
QUADNODES(2,495-482) = 0.04977710; |
| 905 |
QUADNODES(2,496-482) = 0.4502229; |
| 906 |
QUADNODES(2,497-482) = 0.1837304; |
| 907 |
QUADNODES(2,498-482) = 0.3162696; |
| 908 |
QUADNODES(2,499-482) = 0.1837304; |
| 909 |
QUADNODES(2,500-482) = 0.3162696; |
| 910 |
QUADNODES(2,501-482) = 0.1837304; |
| 911 |
QUADNODES(2,502-482) = 0.3162696; |
| 912 |
QUADNODES(2,503-482) = 0.2319011; |
| 913 |
QUADNODES(2,504-482) = 0.02291779; |
| 914 |
QUADNODES(2,505-482) = 0.2319011; |
| 915 |
QUADNODES(2,506-482) = 0.2319011; |
| 916 |
QUADNODES(2,507-482) = 0.5132800; |
| 917 |
QUADNODES(2,508-482) = 0.2319011; |
| 918 |
QUADNODES(2,509-482) = 0.02291779; |
| 919 |
QUADNODES(2,510-482) = 0.2319011; |
| 920 |
QUADNODES(2,511-482) = 0.5132800; |
| 921 |
QUADNODES(2,512-482) = 0.2319011; |
| 922 |
QUADNODES(2,513-482) = 0.5132800; |
| 923 |
QUADNODES(2,514-482) = 0.02291779; |
| 924 |
QUADNODES(2,515-482) = 0.03797005; |
| 925 |
QUADNODES(2,516-482) = 0.7303134; |
| 926 |
QUADNODES(2,517-482) = 0.03797005; |
| 927 |
QUADNODES(2,518-482) = 0.03797005; |
| 928 |
QUADNODES(2,519-482) = 0.1937465; |
| 929 |
QUADNODES(2,520-482) = 0.03797005; |
| 930 |
QUADNODES(2,521-482) = 0.7303134; |
| 931 |
QUADNODES(2,522-482) = 0.03797005; |
| 932 |
QUADNODES(2,523-482) = 0.1937465; |
| 933 |
QUADNODES(2,524-482) = 0.03797005; |
| 934 |
QUADNODES(2,525-482) = 0.1937465; |
| 935 |
QUADNODES(2,526-482) = 0.7303134; |
| 936 |
|
| 937 |
} else { |
| 938 |
|
| 939 |
/* get scheme on [0.1]^3 */ |
| 940 |
|
| 941 |
Finley_Quad_getNodesHex(numQuadNodes,quadNodes,quadWeights); |
| 942 |
if (! Finley_noError()) return; |
| 943 |
|
| 944 |
/* squeeze it: */ |
| 945 |
for (i=0;i<numQuadNodes;i++) { |
| 946 |
Q1=QUADNODES(0,i); |
| 947 |
Q2=QUADNODES(1,i); |
| 948 |
Q3=QUADNODES(2,i); |
| 949 |
|
| 950 |
JA11= (1./3.)*Q2*Q3-(1./2.)*(Q2+Q3) +1.; |
| 951 |
JA12= (1./3.)*Q1*Q3-(1./2.)*Q1; |
| 952 |
JA13= (1./3.)*Q1*Q2-(1./2.)*Q1; |
| 953 |
JA21= (1./3.)*Q2*Q3-(1./2.)*Q2; |
| 954 |
JA22= (1./3.)*Q1*Q3-(1./2.)*(Q1+Q3) +1.; |
| 955 |
JA23= (1./3.)*Q1*Q2-(1./2.)*Q2; |
| 956 |
JA31= (1./3.)*Q2*Q3-(1./2.)*Q3; |
| 957 |
JA32= (1./3.)*Q1*Q3-(1./2.)*Q3; |
| 958 |
JA33= (1./3.)*Q1*Q2-(1./2.)*(Q1+Q2) +1.; |
| 959 |
DET=JA11*JA22*JA33+JA12*JA23*JA31+JA13*JA21*JA32-JA13*JA22*JA31-JA11*JA23*JA32-JA12*JA21*JA33; |
| 960 |
quadWeights[i]=quadWeights[i]*ABS(DET); |
| 961 |
QUADNODES(0,i)=Q1*((1./3.)*Q2*Q3-(1./2.)*(Q2+Q3)+1.); |
| 962 |
QUADNODES(1,i)=Q2*((1./3.)*Q1*Q3-(1./2.)*(Q1+Q3)+1.); |
| 963 |
QUADNODES(2,i)=Q3*((1./3.)*Q1*Q2-(1./2.)*(Q1+Q2)+1.); |
| 964 |
} |
| 965 |
} |
| 966 |
#undef DIM |
| 967 |
} |
| 968 |
|
| 969 |
/**************************************************************/ |
| 970 |
|
| 971 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for the quad [0.1]^2 */ |
| 972 |
/* as a X-product of a 1D scheme. */ |
| 973 |
|
| 974 |
void Finley_Quad_getNodesRec(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 975 |
char error_msg[LenErrorMsg_MAX]; |
| 976 |
int numQuadNodes1d,i,j,l; |
| 977 |
double *quadNodes1d=NULL,*quadWeights1d=NULL; |
| 978 |
bool_t set=FALSE; |
| 979 |
#define DIM 2 |
| 980 |
|
| 981 |
quadNodes1d=TMPMEMALLOC(numQuadNodes,double); |
| 982 |
quadWeights1d=TMPMEMALLOC(numQuadNodes,double); |
| 983 |
if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) { |
| 984 |
/* find numQuadNodes1d with numQuadNodes1d**2==numQuadNodes: */ |
| 985 |
|
| 986 |
for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) { |
| 987 |
if (numQuadNodes1d*numQuadNodes1d==numQuadNodes) { |
| 988 |
|
| 989 |
/* get 1D scheme: */ |
| 990 |
|
| 991 |
Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d); |
| 992 |
|
| 993 |
/* make 2D scheme: */ |
| 994 |
|
| 995 |
if (Finley_noError()) { |
| 996 |
l=0; |
| 997 |
for (i=0;i<numQuadNodes1d;i++) { |
| 998 |
for (j=0;j<numQuadNodes1d;j++) { |
| 999 |
QUADNODES(0,l)=quadNodes1d[i]; |
| 1000 |
QUADNODES(1,l)=quadNodes1d[j]; |
| 1001 |
QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]; |
| 1002 |
l++; |
| 1003 |
} |
| 1004 |
} |
| 1005 |
set=TRUE; |
| 1006 |
break; |
| 1007 |
} |
| 1008 |
} |
| 1009 |
} |
| 1010 |
if (!set) { |
| 1011 |
sprintf(error_msg,"Finley_Quad_getNodesRec: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
| 1012 |
Finley_setError(VALUE_ERROR,error_msg); |
| 1013 |
} |
| 1014 |
TMPMEMFREE(quadNodes1d); |
| 1015 |
TMPMEMFREE(quadWeights1d); |
| 1016 |
} |
| 1017 |
#undef DIM |
| 1018 |
} |
| 1019 |
|
| 1020 |
/**************************************************************/ |
| 1021 |
|
| 1022 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for the hex [0.1]^3 */ |
| 1023 |
/* as a X-product of a 1D scheme. */ |
| 1024 |
|
| 1025 |
void Finley_Quad_getNodesHex(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 1026 |
char error_msg[LenErrorMsg_MAX]; |
| 1027 |
int numQuadNodes1d,i,j,k,l; |
| 1028 |
double *quadNodes1d=NULL,*quadWeights1d=NULL; |
| 1029 |
bool_t set; |
| 1030 |
#define DIM 3 |
| 1031 |
|
| 1032 |
/* find numQuadNodes1d with numQuadNodes1d**3==numQuadNodes: */ |
| 1033 |
|
| 1034 |
quadNodes1d=TMPMEMALLOC(numQuadNodes,double); |
| 1035 |
quadWeights1d=TMPMEMALLOC(numQuadNodes,double); |
| 1036 |
if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) { |
| 1037 |
for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) { |
| 1038 |
if (numQuadNodes1d*numQuadNodes1d*numQuadNodes1d==numQuadNodes) { |
| 1039 |
|
| 1040 |
/* get 1D scheme: */ |
| 1041 |
|
| 1042 |
Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d); |
| 1043 |
|
| 1044 |
/* make 3D scheme: */ |
| 1045 |
|
| 1046 |
if (Finley_noError()) { |
| 1047 |
l=0; |
| 1048 |
for (i=0;i<numQuadNodes1d;i++) { |
| 1049 |
for (j=0;j<numQuadNodes1d;j++) { |
| 1050 |
for (k=0;k<numQuadNodes1d;k++) { |
| 1051 |
QUADNODES(0,l)=quadNodes1d[i]; |
| 1052 |
QUADNODES(1,l)=quadNodes1d[j]; |
| 1053 |
QUADNODES(2,l)=quadNodes1d[k]; |
| 1054 |
QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]*quadWeights1d[k]; |
| 1055 |
l++; |
| 1056 |
} |
| 1057 |
} |
| 1058 |
} |
| 1059 |
set=TRUE; |
| 1060 |
break; |
| 1061 |
} |
| 1062 |
} |
| 1063 |
} |
| 1064 |
if (!set) { |
| 1065 |
sprintf(error_msg,"Finley_Quad_getNodesHex: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
| 1066 |
Finley_setError(VALUE_ERROR,error_msg); |
| 1067 |
} |
| 1068 |
TMPMEMFREE(quadNodes1d); |
| 1069 |
TMPMEMFREE(quadWeights1d); |
| 1070 |
} |
| 1071 |
#undef DIM |
| 1072 |
} |
| 1073 |
|
| 1074 |
/**************************************************************/ |
| 1075 |
|
| 1076 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for a point. As there */ |
| 1077 |
/* in no quadrature scheme for a point any value for numQuadNodes other than 0 throws */ |
| 1078 |
/* an error. */ |
| 1079 |
|
| 1080 |
void Finley_Quad_getNodesPoint(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 1081 |
if (numQuadNodes!=0) { |
| 1082 |
Finley_setError(VALUE_ERROR,"Finley_Quad_getNodesPoint: There is no quadrature scheme on points."); |
| 1083 |
} |
| 1084 |
} |
| 1085 |
|
| 1086 |
/**************************************************************/ |
| 1087 |
|
| 1088 |
/* get a quadrature scheme with numQuadNodes quadrature nodes on the line [0,1]: */ |
| 1089 |
/* The nodes and weights are set from a table. */ |
| 1090 |
|
| 1091 |
void Finley_Quad_getNodesLine(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 1092 |
switch(numQuadNodes) { |
| 1093 |
case 1: |
| 1094 |
quadNodes[0]=0.5; |
| 1095 |
quadWeights[0]=1.; |
| 1096 |
break; |
| 1097 |
|
| 1098 |
case 2: |
| 1099 |
quadNodes[0]=(1.-.577350269189626)/2.; |
| 1100 |
quadNodes[1]=(1.+.577350269189626)/2.; |
| 1101 |
quadWeights[0]=.5; |
| 1102 |
quadWeights[1]=.5; |
| 1103 |
break; |
| 1104 |
|
| 1105 |
case 3: |
| 1106 |
quadNodes[0]=(1.-.774596669241483)/2.; |
| 1107 |
quadNodes[1]=.5; |
| 1108 |
quadNodes[2]=(1.+.774596669241483)/2.; |
| 1109 |
quadWeights[0]=5./18.; |
| 1110 |
quadWeights[1]=4./ 9.; |
| 1111 |
quadWeights[2]=5./18.; |
| 1112 |
break; |
| 1113 |
|
| 1114 |
case 4: |
| 1115 |
quadNodes[0]=(1.-.861136311594053)/2.; |
| 1116 |
quadNodes[1]=(1.-.339981043584856)/2.; |
| 1117 |
quadNodes[2]=(1.+.339981043584856)/2.; |
| 1118 |
quadNodes[3]=(1.+.861136311594053)/2.; |
| 1119 |
quadWeights[0]=.347854845137454/2.; |
| 1120 |
quadWeights[1]=.652145154862546/2.; |
| 1121 |
quadWeights[2]=.652145154862546/2.; |
| 1122 |
quadWeights[3]=.347854845137454/2.; |
| 1123 |
break; |
| 1124 |
|
| 1125 |
case 5: |
| 1126 |
quadNodes[0]=(1.-.906179845938664)/2.; |
| 1127 |
quadNodes[1]=(1.-.538469310105683)/2.; |
| 1128 |
quadNodes[2]= .5; |
| 1129 |
quadNodes[3]=(1.+.538469310105683)/2.; |
| 1130 |
quadNodes[4]=(1.+.906179845938664)/2.; |
| 1131 |
quadWeights[0]=.236926885056189/2.; |
| 1132 |
quadWeights[1]=.478628670499366/2.; |
| 1133 |
quadWeights[2]=.568888888888889/2.; |
| 1134 |
quadWeights[3]=.478628670499366/2.; |
| 1135 |
quadWeights[4]=.236926885056189/2.; |
| 1136 |
break; |
| 1137 |
|
| 1138 |
case 6: |
| 1139 |
quadNodes[0]=(1.-.932469514203152)/2.; |
| 1140 |
quadNodes[1]=(1.-.661209386466265)/2.; |
| 1141 |
quadNodes[2]=(1.-.238619186083197)/2.; |
| 1142 |
quadNodes[3]=(1.+.238619186083197)/2.; |
| 1143 |
quadNodes[4]=(1.+.661209386466265)/2.; |
| 1144 |
quadNodes[5]=(1.+.932469514203152)/2.; |
| 1145 |
quadWeights[0]=.171324492379170/2.; |
| 1146 |
quadWeights[1]=.360761573048139/2.; |
| 1147 |
quadWeights[2]=.467913934572691/2.; |
| 1148 |
quadWeights[3]=.467913934572691/2.; |
| 1149 |
quadWeights[4]=.360761573048139/2.; |
| 1150 |
quadWeights[5]=.171324492379170/2.; |
| 1151 |
break; |
| 1152 |
|
| 1153 |
case 7: |
| 1154 |
quadNodes[0]=(1.-.949107912342759)/2.; |
| 1155 |
quadNodes[1]=(1.-.741531185599394)/2.; |
| 1156 |
quadNodes[2]=(1.-.405845151377397)/2.; |
| 1157 |
quadNodes[3]=0.5; |
| 1158 |
quadNodes[4]=(1.+.405845151377397)/2.; |
| 1159 |
quadNodes[5]=(1.+.741531185599394)/2.; |
| 1160 |
quadNodes[6]=(1.+.949107912342759)/2.; |
| 1161 |
quadWeights[0]= .129484966168870/2.; |
| 1162 |
quadWeights[1]= .279705391489277/2.; |
| 1163 |
quadWeights[2]= .381830050505119/2.; |
| 1164 |
quadWeights[3]= .417959183673469/2.; |
| 1165 |
quadWeights[4]= .381830050505119/2.; |
| 1166 |
quadWeights[5]= .279705391489277/2.; |
| 1167 |
quadWeights[6]= .129484966168870/2.; |
| 1168 |
break; |
| 1169 |
|
| 1170 |
case 8: |
| 1171 |
quadNodes[0]=(1.-.960289856497536)/2.; |
| 1172 |
quadNodes[1]=(1.-.796666477413627)/2.; |
| 1173 |
quadNodes[2]=(1.-.525532409916329)/2.; |
| 1174 |
quadNodes[3]=(1.-.183434642495650)/2.; |
| 1175 |
quadNodes[4]=(1.+.183434642495650)/2.; |
| 1176 |
quadNodes[5]=(1.+.525532409916329)/2.; |
| 1177 |
quadNodes[6]=(1.+.796666477413627)/2.; |
| 1178 |
quadNodes[7]=(1.+.960289856497536)/2.; |
| 1179 |
quadWeights[0]= .101228536290376/2.; |
| 1180 |
quadWeights[1]= .222381034453374/2.; |
| 1181 |
quadWeights[2]= .313706645877887/2.; |
| 1182 |
quadWeights[3]= .362683783378362/2.; |
| 1183 |
quadWeights[4]= .362683783378362/2.; |
| 1184 |
quadWeights[5]= .313706645877887/2.; |
| 1185 |
quadWeights[6]= .222381034453374/2.; |
| 1186 |
quadWeights[7]= .101228536290376/2.; |
| 1187 |
break; |
| 1188 |
|
| 1189 |
case 9: |
| 1190 |
quadNodes[0]=(1.-.968160239507626)/2.; |
| 1191 |
quadNodes[1]=(1.-.836031107326636)/2.; |
| 1192 |
quadNodes[2]=(1.-.613371432700590)/2.; |
| 1193 |
quadNodes[3]=(1.-.324253423403809)/2.; |
| 1194 |
quadNodes[4]= .5; |
| 1195 |
quadNodes[5]=(1.+.324253423403809)/2.; |
| 1196 |
quadNodes[6]=(1.+.613371432700590)/2.; |
| 1197 |
quadNodes[7]=(1.+.836031107326636)/2.; |
| 1198 |
quadNodes[8]=(1.+.968160239507626)/2.; |
| 1199 |
quadWeights[0]= .081274388361574/2.; |
| 1200 |
quadWeights[1]= .180648160694857/2.; |
| 1201 |
quadWeights[2]= .260610696402935/2.; |
| 1202 |
quadWeights[3]= .312347077040003/2.; |
| 1203 |
quadWeights[4]= .330239355001260/2.; |
| 1204 |
quadWeights[5]= .312347077040003/2.; |
| 1205 |
quadWeights[6]= .260610696402935/2.; |
| 1206 |
quadWeights[7]= .180648160694857/2.; |
| 1207 |
quadWeights[8]= .081274388361574/2.; |
| 1208 |
break; |
| 1209 |
|
| 1210 |
case 10: |
| 1211 |
quadNodes[0]=(1.-.973906528517172)/2.; |
| 1212 |
quadNodes[1]=(1.-.865063366688985)/2.; |
| 1213 |
quadNodes[2]=(1.-.679409568299024)/2.; |
| 1214 |
quadNodes[3]=(1.-.433395394129247)/2.; |
| 1215 |
quadNodes[4]=(1.-.148874338981631)/2.; |
| 1216 |
quadNodes[5]=(1.+.148874338981631)/2.; |
| 1217 |
quadNodes[6]=(1.+.433395394129247)/2.; |
| 1218 |
quadNodes[7]=(1.+.679409568299024)/2.; |
| 1219 |
quadNodes[8]=(1.+.865063366688985)/2.; |
| 1220 |
quadNodes[9]=(1.+.973906528517172)/2.; |
| 1221 |
quadWeights[0]= .066671344308688/2.; |
| 1222 |
quadWeights[1]= .149451349150581/2.; |
| 1223 |
quadWeights[2]= .219086362515982/2.; |
| 1224 |
quadWeights[3]= .269266719309996/2.; |
| 1225 |
quadWeights[4]= .295524224714753/2.; |
| 1226 |
quadWeights[5]= .295524224714753/2.; |
| 1227 |
quadWeights[6]= .269266719309996/2.; |
| 1228 |
quadWeights[7]= .219086362515982/2.; |
| 1229 |
quadWeights[8]= .149451349150581/2.; |
| 1230 |
quadWeights[9]= .066671344308688/2.; |
| 1231 |
break; |
| 1232 |
|
| 1233 |
default: |
| 1234 |
Finley_setError(VALUE_ERROR,"__FILE__: Negative intergration order."); |
| 1235 |
break; |
| 1236 |
} |
| 1237 |
} |
| 1238 |
/**************************************************************/ |
| 1239 |
/* */ |
| 1240 |
/* the following function are used define the meshes on the surface in the xy-plane */ |
| 1241 |
|
| 1242 |
/* triangle surface on a tetrahedron */ |
| 1243 |
void Finley_Quad_getNodesTriOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 1244 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesTri); |
| 1245 |
} |
| 1246 |
/* rectangular surface on a hexahedron */ |
| 1247 |
void Finley_Quad_getNodesRecOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 1248 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesRec); |
| 1249 |
} |
| 1250 |
/* line surface on a triangle or rectangle */ |
| 1251 |
void Finley_Quad_getNodesLineOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 1252 |
Finley_Quad_makeNodesOnFace(2,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesLine); |
| 1253 |
} |
| 1254 |
/* point surface on a line */ |
| 1255 |
void Finley_Quad_getNodesPointOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 1256 |
Finley_Quad_makeNodesOnFace(1,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesPoint); |
| 1257 |
} |
| 1258 |
|
| 1259 |
void Finley_Quad_makeNodesOnFace(int dim, int numQuadNodes,double* quadNodes,double* quadWeights, Finley_Quad_getNodes getFaceNodes) { |
| 1260 |
int q,i; |
| 1261 |
double *quadNodesOnFace=NULL; |
| 1262 |
#define DIM dim |
| 1263 |
quadNodesOnFace=TMPMEMALLOC(numQuadNodes*(dim-1),double); |
| 1264 |
|
| 1265 |
if (! Finley_checkPtr(quadNodesOnFace) ) { |
| 1266 |
getFaceNodes(numQuadNodes,quadNodesOnFace,quadWeights); |
| 1267 |
if (Finley_noError()) { |
| 1268 |
for (q=0;q<numQuadNodes;q++) { |
| 1269 |
for (i=0;i<dim-1;i++) QUADNODES(i,q)=quadNodesOnFace[INDEX2(i,q,dim-1)]; |
| 1270 |
QUADNODES(dim-1,q)=0; |
| 1271 |
} |
| 1272 |
} |
| 1273 |
TMPMEMFREE(quadNodesOnFace); |
| 1274 |
} |
| 1275 |
#undef DIM |
| 1276 |
} |
| 1277 |
|
| 1278 |
/**************************************************************/ |
| 1279 |
|
| 1280 |
/* The following functions Finley_Quad_getNumNodes* return the nmber of quadrature points needed to */ |
| 1281 |
/* achieve a certain accuracy. Notice that for Tet and Tri the the order is increased */ |
| 1282 |
/* to consider the accuracy reduction through the construction process. */ |
| 1283 |
|
| 1284 |
|
| 1285 |
int Finley_Quad_getNumNodesPoint(int order) { |
| 1286 |
if (order <0 ) { |
| 1287 |
Finley_setError(VALUE_ERROR,"Finley_Quad_getNumNodesPoint: Negative intergration order."); |
| 1288 |
return -1; |
| 1289 |
} else { |
| 1290 |
return 0; |
| 1291 |
} |
| 1292 |
} |
| 1293 |
|
| 1294 |
int Finley_Quad_getNumNodesLine(int order) { |
| 1295 |
char error_msg[LenErrorMsg_MAX]; |
| 1296 |
if (order <0 ) { |
| 1297 |
Finley_setError(VALUE_ERROR,"Finley_Quad_getNumNodesPoint: Negative intergration order."); |
| 1298 |
return -1; |
| 1299 |
} else { |
| 1300 |
if (order > 2*MAX_numQuadNodesLine-1) { |
| 1301 |
sprintf(error_msg,"Finley_Quad_getNumNodesPoint: requested integration order %d on line is too large (>%d).", |
| 1302 |
order,2*MAX_numQuadNodesLine-1); |
| 1303 |
Finley_setError(VALUE_ERROR,error_msg); |
| 1304 |
return -1; |
| 1305 |
} else { |
| 1306 |
Finley_resetError(); |
| 1307 |
return order/2+1; |
| 1308 |
} |
| 1309 |
} |
| 1310 |
} |
| 1311 |
|
| 1312 |
int Finley_Quad_getNumNodesTri(int order) { |
| 1313 |
int numQuadNodesLine; |
| 1314 |
if (order<=1) { |
| 1315 |
return 1; |
| 1316 |
} else if (order<=2){ |
| 1317 |
return 3; |
| 1318 |
} else if (order<=3){ |
| 1319 |
return 4; |
| 1320 |
} else if (order<=4){ |
| 1321 |
return 6; |
| 1322 |
} else if (order<=5){ |
| 1323 |
return 7; |
| 1324 |
} else if (order<=6){ |
| 1325 |
return 12; |
| 1326 |
} else if (order<=7){ |
| 1327 |
return 13; |
| 1328 |
} else if (order<=8){ |
| 1329 |
return 16; |
| 1330 |
} else if (order<=9){ |
| 1331 |
return 19; |
| 1332 |
} else { |
| 1333 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+1); |
| 1334 |
if (Finley_noError()) { |
| 1335 |
return numQuadNodesLine*numQuadNodesLine; |
| 1336 |
} else { |
| 1337 |
return -1; |
| 1338 |
} |
| 1339 |
} |
| 1340 |
} |
| 1341 |
|
| 1342 |
int Finley_Quad_getNumNodesRec(int order) { |
| 1343 |
int numQuadNodesLine; |
| 1344 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
| 1345 |
if (Finley_noError()) { |
| 1346 |
return numQuadNodesLine*numQuadNodesLine; |
| 1347 |
} else { |
| 1348 |
return -1; |
| 1349 |
} |
| 1350 |
} |
| 1351 |
|
| 1352 |
int Finley_Quad_getNumNodesTet(int order) { |
| 1353 |
int numQuadNodesLine; |
| 1354 |
if (order<=1) { |
| 1355 |
return 1; |
| 1356 |
} else if (order<=2){ |
| 1357 |
return 4; |
| 1358 |
} else if (order<=3){ |
| 1359 |
return 5; |
| 1360 |
} else if (order<=4){ |
| 1361 |
return 11; |
| 1362 |
} else if (order<=5){ |
| 1363 |
return 15; |
| 1364 |
} else if (order<=6){ |
| 1365 |
return 24; |
| 1366 |
} else if (order<=7){ |
| 1367 |
return 31; |
| 1368 |
} else if (order<=8){ |
| 1369 |
return 45; |
| 1370 |
} else { |
| 1371 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+2); |
| 1372 |
if (Finley_noError()) { |
| 1373 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
| 1374 |
} else { |
| 1375 |
return -1; |
| 1376 |
} |
| 1377 |
} |
| 1378 |
} |
| 1379 |
|
| 1380 |
int Finley_Quad_getNumNodesHex(int order) { |
| 1381 |
int numQuadNodesLine; |
| 1382 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
| 1383 |
if (Finley_noError()) { |
| 1384 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
| 1385 |
} else { |
| 1386 |
return -1; |
| 1387 |
} |
| 1388 |
} |
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