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/* |
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************************************************************ |
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* Copyright 2006 by ACcESS MNRF * |
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* * |
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* http://www.access.edu.au * |
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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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/* Author: gross@access.edu.au */ |
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/* Version: $Id$ */ |
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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; |
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#define DIM 2 |
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|
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/* the easy case: */ |
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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)= .5; |
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} else { |
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|
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/* get scheme on [0.1]^2 */ |
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|
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Finley_Quad_getNodesRec(numQuadNodes,quadNodes,quadWeights); |
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if (! Finley_noError()) return; |
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|
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/* squeeze it: */ |
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|
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for (i=0;i<numQuadNodes;i++) { |
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Q1=QUADNODES(0,i); |
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Q2=QUADNODES(1,i); |
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QUADWEIGHTS(i)=QUADWEIGHTS(i)*(1.-(1./2.)*(Q1+Q2)); |
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QUADNODES(0,i)=Q1*(1.-(1./2.)*Q2); |
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QUADNODES(1,i)=Q2*(1.-(1./2.)*Q1); |
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} |
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} |
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#undef DIM |
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} |
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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 tet */ |
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/* as a queezed scheme on a hex [0,1]^3 */ |
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|
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void Finley_Quad_getNodesTet(int numQuadNodes,double* quadNodes,double* quadWeights) { |
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int i; |
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double Q1,Q2,Q3,JA11,JA12,JA13,JA21,JA22,JA23,JA31,JA32,JA33,DET; |
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#define DIM 3 |
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|
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/* the easy case: */ |
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|
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if (numQuadNodes==1) { |
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QUADNODES(0,0)= .25; |
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QUADNODES(1,0)= .25; |
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QUADNODES(2,0)= .25; |
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QUADWEIGHTS(0)=1./6.; |
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} else { |
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|
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/* get scheme on [0.1]^3 */ |
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|
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Finley_Quad_getNodesHex(numQuadNodes,quadNodes,quadWeights); |
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if (! Finley_noError()) return; |
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|
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/* squeeze it: */ |
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|
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for (i=0;i<numQuadNodes;i++) { |
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Q1=QUADNODES(0,i); |
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Q2=QUADNODES(1,i); |
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Q3=QUADNODES(2,i); |
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|
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JA11= (1./3.)*Q2*Q3-(1./2.)*(Q2+Q3) +1.; |
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JA12= (1./3.)*Q1*Q3-(1./2.)*Q1; |
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JA13= (1./3.)*Q1*Q2-(1./2.)*Q1; |
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JA21= (1./3.)*Q2*Q3-(1./2.)*Q2; |
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JA22= (1./3.)*Q1*Q3-(1./2.)*(Q1+Q3) +1.; |
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JA23= (1./3.)*Q1*Q2-(1./2.)*Q2; |
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JA31= (1./3.)*Q2*Q3-(1./2.)*Q3; |
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JA32= (1./3.)*Q1*Q3-(1./2.)*Q3; |
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JA33= (1./3.)*Q1*Q2-(1./2.)*(Q1+Q2) +1.; |
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DET=JA11*JA22*JA33+JA12*JA23*JA31+JA13*JA21*JA32-JA13*JA22*JA31-JA11*JA23*JA32-JA12*JA21*JA33; |
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quadWeights[i]=quadWeights[i]*ABS(DET); |
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QUADNODES(0,i)=Q1*((1./3.)*Q2*Q3-(1./2.)*(Q2+Q3)+1.); |
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QUADNODES(1,i)=Q2*((1./3.)*Q1*Q3-(1./2.)*(Q1+Q3)+1.); |
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QUADNODES(2,i)=Q3*((1./3.)*Q1*Q2-(1./2.)*(Q1+Q2)+1.); |
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} |
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} |
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#undef DIM |
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} |
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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 quad [0.1]^2 */ |
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/* as a X-product of a 1D scheme. */ |
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|
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void Finley_Quad_getNodesRec(int numQuadNodes,double* quadNodes,double* quadWeights) { |
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char error_msg[LenErrorMsg_MAX]; |
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int numQuadNodes1d,i,j,l; |
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double *quadNodes1d=NULL,*quadWeights1d=NULL; |
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bool_t set=FALSE; |
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#define DIM 2 |
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|
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quadNodes1d=TMPMEMALLOC(numQuadNodes,double); |
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quadWeights1d=TMPMEMALLOC(numQuadNodes,double); |
129 |
if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) { |
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/* find numQuadNodes1d with numQuadNodes1d**2==numQuadNodes: */ |
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|
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for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) { |
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if (numQuadNodes1d*numQuadNodes1d==numQuadNodes) { |
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|
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/* get 1D scheme: */ |
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|
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Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d); |
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|
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/* make 2D scheme: */ |
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|
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if (Finley_noError()) { |
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l=0; |
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for (i=0;i<numQuadNodes1d;i++) { |
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for (j=0;j<numQuadNodes1d;j++) { |
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QUADNODES(0,l)=quadNodes1d[i]; |
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QUADNODES(1,l)=quadNodes1d[j]; |
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QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]; |
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l++; |
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} |
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} |
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set=TRUE; |
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break; |
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} |
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} |
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} |
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if (!set) { |
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sprintf(error_msg,"Finley_Quad_getNodesRec: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
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Finley_setError(VALUE_ERROR,error_msg); |
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} |
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TMPMEMFREE(quadNodes1d); |
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TMPMEMFREE(quadWeights1d); |
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} |
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#undef DIM |
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} |
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|
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/**************************************************************/ |
167 |
|
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/* get a quadrature scheme with numQuadNodes quadrature nodes for the hex [0.1]^3 */ |
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/* as a X-product of a 1D scheme. */ |
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|
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void Finley_Quad_getNodesHex(int numQuadNodes,double* quadNodes,double* quadWeights) { |
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char error_msg[LenErrorMsg_MAX]; |
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int numQuadNodes1d,i,j,k,l; |
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double *quadNodes1d=NULL,*quadWeights1d=NULL; |
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bool_t set; |
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#define DIM 3 |
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|
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/* find numQuadNodes1d with numQuadNodes1d**3==numQuadNodes: */ |
179 |
|
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quadNodes1d=TMPMEMALLOC(numQuadNodes,double); |
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quadWeights1d=TMPMEMALLOC(numQuadNodes,double); |
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if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) { |
183 |
for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) { |
184 |
if (numQuadNodes1d*numQuadNodes1d*numQuadNodes1d==numQuadNodes) { |
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|
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/* get 1D scheme: */ |
187 |
|
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Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d); |
189 |
|
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/* make 3D scheme: */ |
191 |
|
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if (Finley_noError()) { |
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l=0; |
194 |
for (i=0;i<numQuadNodes1d;i++) { |
195 |
for (j=0;j<numQuadNodes1d;j++) { |
196 |
for (k=0;k<numQuadNodes1d;k++) { |
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QUADNODES(0,l)=quadNodes1d[i]; |
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QUADNODES(1,l)=quadNodes1d[j]; |
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QUADNODES(2,l)=quadNodes1d[k]; |
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QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]*quadWeights1d[k]; |
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l++; |
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} |
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} |
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} |
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set=TRUE; |
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break; |
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} |
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} |
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} |
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if (!set) { |
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sprintf(error_msg,"Finley_Quad_getNodesHex: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
212 |
Finley_setError(VALUE_ERROR,error_msg); |
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} |
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TMPMEMFREE(quadNodes1d); |
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TMPMEMFREE(quadWeights1d); |
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} |
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#undef DIM |
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} |
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|
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/**************************************************************/ |
221 |
|
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/* get a quadrature scheme with numQuadNodes quadrature nodes for a point. As there */ |
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/* in no quadrature scheme for a point any value for numQuadNodes other than 0 throws */ |
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/* an error. */ |
225 |
|
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void Finley_Quad_getNodesPoint(int numQuadNodes,double* quadNodes,double* quadWeights) { |
227 |
if (numQuadNodes!=0) { |
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Finley_setError(VALUE_ERROR,"Finley_Quad_getNodesPoint: There is no quadrature scheme on points."); |
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} |
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} |
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|
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/**************************************************************/ |
233 |
|
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/* get a quadrature scheme with numQuadNodes quadrature nodes on the line [0,1]: */ |
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/* The nodes and weights are set from a table. */ |
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|
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void Finley_Quad_getNodesLine(int numQuadNodes,double* quadNodes,double* quadWeights) { |
238 |
switch(numQuadNodes) { |
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case 1: |
240 |
quadNodes[0]=0.5; |
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quadWeights[0]=1.; |
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break; |
243 |
|
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case 2: |
245 |
quadNodes[0]=(1.-.577350269189626)/2.; |
246 |
quadNodes[1]=(1.+.577350269189626)/2.; |
247 |
quadWeights[0]=.5; |
248 |
quadWeights[1]=.5; |
249 |
break; |
250 |
|
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case 3: |
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quadNodes[0]=(1.-.774596669241483)/2.; |
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quadNodes[1]=.5; |
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quadNodes[2]=(1.+.774596669241483)/2.; |
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quadWeights[0]=5./18.; |
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quadWeights[1]=4./ 9.; |
257 |
quadWeights[2]=5./18.; |
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break; |
259 |
|
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case 4: |
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quadNodes[0]=(1.-.861136311594053)/2.; |
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quadNodes[1]=(1.-.339981043584856)/2.; |
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quadNodes[2]=(1.+.339981043584856)/2.; |
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quadNodes[3]=(1.+.861136311594053)/2.; |
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quadWeights[0]=.347854845137454/2.; |
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quadWeights[1]=.652145154862546/2.; |
267 |
quadWeights[2]=.652145154862546/2.; |
268 |
quadWeights[3]=.347854845137454/2.; |
269 |
break; |
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|
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case 5: |
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quadNodes[0]=(1.-.906179845938664)/2.; |
273 |
quadNodes[1]=(1.-.538469310105683)/2.; |
274 |
quadNodes[2]= .5; |
275 |
quadNodes[3]=(1.+.538469310105683)/2.; |
276 |
quadNodes[4]=(1.+.906179845938664)/2.; |
277 |
quadWeights[0]=.236926885056189/2.; |
278 |
quadWeights[1]=.478628670499366/2.; |
279 |
quadWeights[2]=.568888888888889/2.; |
280 |
quadWeights[3]=.478628670499366/2.; |
281 |
quadWeights[4]=.236926885056189/2.; |
282 |
break; |
283 |
|
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case 6: |
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quadNodes[0]=(1.-.932469514203152)/2.; |
286 |
quadNodes[1]=(1.-.661209386466265)/2.; |
287 |
quadNodes[2]=(1.-.238619186083197)/2.; |
288 |
quadNodes[3]=(1.+.238619186083197)/2.; |
289 |
quadNodes[4]=(1.+.661209386466265)/2.; |
290 |
quadNodes[5]=(1.+.932469514203152)/2.; |
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quadWeights[0]=.171324492379170/2.; |
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quadWeights[1]=.360761573048139/2.; |
293 |
quadWeights[2]=.467913934572691/2.; |
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quadWeights[3]=.467913934572691/2.; |
295 |
quadWeights[4]=.360761573048139/2.; |
296 |
quadWeights[5]=.171324492379170/2.; |
297 |
break; |
298 |
|
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case 7: |
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quadNodes[0]=(1.-.949107912342759)/2.; |
301 |
quadNodes[1]=(1.-.741531185599394)/2.; |
302 |
quadNodes[2]=(1.-.405845151377397)/2.; |
303 |
quadNodes[3]=0.5; |
304 |
quadNodes[4]=(1.+.405845151377397)/2.; |
305 |
quadNodes[5]=(1.+.741531185599394)/2.; |
306 |
quadNodes[6]=(1.+.949107912342759)/2.; |
307 |
quadWeights[0]= .129484966168870/2.; |
308 |
quadWeights[1]= .279705391489277/2.; |
309 |
quadWeights[2]= .381830050505119/2.; |
310 |
quadWeights[3]= .417959183673469/2.; |
311 |
quadWeights[4]= .381830050505119/2.; |
312 |
quadWeights[5]= .279705391489277/2.; |
313 |
quadWeights[6]= .129484966168870/2.; |
314 |
break; |
315 |
|
316 |
case 8: |
317 |
quadNodes[0]=(1.-.960289856497536)/2.; |
318 |
quadNodes[1]=(1.-.796666477413627)/2.; |
319 |
quadNodes[2]=(1.-.525532409916329)/2.; |
320 |
quadNodes[3]=(1.-.183434642495650)/2.; |
321 |
quadNodes[4]=(1.+.183434642495650)/2.; |
322 |
quadNodes[5]=(1.+.525532409916329)/2.; |
323 |
quadNodes[6]=(1.+.796666477413627)/2.; |
324 |
quadNodes[7]=(1.+.960289856497536)/2.; |
325 |
quadWeights[0]= .101228536290376/2.; |
326 |
quadWeights[1]= .222381034453374/2.; |
327 |
quadWeights[2]= .313706645877887/2.; |
328 |
quadWeights[3]= .362683783378362/2.; |
329 |
quadWeights[4]= .362683783378362/2.; |
330 |
quadWeights[5]= .313706645877887/2.; |
331 |
quadWeights[6]= .222381034453374/2.; |
332 |
quadWeights[7]= .101228536290376/2.; |
333 |
break; |
334 |
|
335 |
case 9: |
336 |
quadNodes[0]=(1.-.968160239507626)/2.; |
337 |
quadNodes[1]=(1.-.836031107326636)/2.; |
338 |
quadNodes[2]=(1.-.613371432700590)/2.; |
339 |
quadNodes[3]=(1.-.324253423403809)/2.; |
340 |
quadNodes[4]= .5; |
341 |
quadNodes[5]=(1.+.324253423403809)/2.; |
342 |
quadNodes[6]=(1.+.613371432700590)/2.; |
343 |
quadNodes[7]=(1.+.836031107326636)/2.; |
344 |
quadNodes[8]=(1.+.968160239507626)/2.; |
345 |
quadWeights[0]= .081274388361574/2.; |
346 |
quadWeights[1]= .180648160694857/2.; |
347 |
quadWeights[2]= .260610696402935/2.; |
348 |
quadWeights[3]= .312347077040003/2.; |
349 |
quadWeights[4]= .330239355001260/2.; |
350 |
quadWeights[5]= .312347077040003/2.; |
351 |
quadWeights[6]= .260610696402935/2.; |
352 |
quadWeights[7]= .180648160694857/2.; |
353 |
quadWeights[8]= .081274388361574/2.; |
354 |
break; |
355 |
|
356 |
case 10: |
357 |
quadNodes[0]=(1.-.973906528517172)/2.; |
358 |
quadNodes[1]=(1.-.865063366688985)/2.; |
359 |
quadNodes[2]=(1.-.679409568299024)/2.; |
360 |
quadNodes[3]=(1.-.433395394129247)/2.; |
361 |
quadNodes[4]=(1.-.148874338981631)/2.; |
362 |
quadNodes[5]=(1.+.148874338981631)/2.; |
363 |
quadNodes[6]=(1.+.433395394129247)/2.; |
364 |
quadNodes[7]=(1.+.679409568299024)/2.; |
365 |
quadNodes[8]=(1.+.865063366688985)/2.; |
366 |
quadNodes[9]=(1.+.973906528517172)/2.; |
367 |
quadWeights[0]= .066671344308688/2.; |
368 |
quadWeights[1]= .149451349150581/2.; |
369 |
quadWeights[2]= .219086362515982/2.; |
370 |
quadWeights[3]= .269266719309996/2.; |
371 |
quadWeights[4]= .295524224714753/2.; |
372 |
quadWeights[5]= .295524224714753/2.; |
373 |
quadWeights[6]= .269266719309996/2.; |
374 |
quadWeights[7]= .219086362515982/2.; |
375 |
quadWeights[8]= .149451349150581/2.; |
376 |
quadWeights[9]= .066671344308688/2.; |
377 |
break; |
378 |
|
379 |
default: |
380 |
Finley_setError(VALUE_ERROR,"__FILE__: Negative intergration order."); |
381 |
break; |
382 |
} |
383 |
} |
384 |
/**************************************************************/ |
385 |
/* */ |
386 |
/* the following function are used define the meshes on the surface in the xy-plane */ |
387 |
|
388 |
/* triangle surface on a tetrahedron */ |
389 |
void Finley_Quad_getNodesTriOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
390 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesTri); |
391 |
} |
392 |
/* rectangular surface on a hexahedron */ |
393 |
void Finley_Quad_getNodesRecOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
394 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesRec); |
395 |
} |
396 |
/* line surface on a triangle or rectangle */ |
397 |
void Finley_Quad_getNodesLineOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
398 |
Finley_Quad_makeNodesOnFace(2,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesLine); |
399 |
} |
400 |
/* point surface on a line */ |
401 |
void Finley_Quad_getNodesPointOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
402 |
Finley_Quad_makeNodesOnFace(1,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesPoint); |
403 |
} |
404 |
|
405 |
void Finley_Quad_makeNodesOnFace(int dim, int numQuadNodes,double* quadNodes,double* quadWeights, Finley_Quad_getNodes getFaceNodes) { |
406 |
int q,i; |
407 |
double *quadNodesOnFace=NULL; |
408 |
#define DIM dim |
409 |
quadNodesOnFace=TMPMEMALLOC(numQuadNodes*(dim-1),double); |
410 |
|
411 |
if (! Finley_checkPtr(quadNodesOnFace) ) { |
412 |
getFaceNodes(numQuadNodes,quadNodesOnFace,quadWeights); |
413 |
if (Finley_noError()) { |
414 |
for (q=0;q<numQuadNodes;q++) { |
415 |
for (i=0;i<dim-1;i++) QUADNODES(i,q)=quadNodesOnFace[INDEX2(i,q,dim-1)]; |
416 |
QUADNODES(dim-1,q)=0; |
417 |
} |
418 |
} |
419 |
TMPMEMFREE(quadNodesOnFace); |
420 |
} |
421 |
#undef DIM |
422 |
} |
423 |
|
424 |
/**************************************************************/ |
425 |
|
426 |
/* The following functions Finley_Quad_getNumNodes* return the nmber of quadrature points needed to */ |
427 |
/* achieve a certain accuracy. Notice that for Tet and Tri the the order is increased */ |
428 |
/* to consider the accuracy reduction through the construction process. */ |
429 |
|
430 |
|
431 |
int Finley_Quad_getNumNodesPoint(int order) { |
432 |
if (order <0 ) { |
433 |
Finley_setError(VALUE_ERROR,"Finley_Quad_getNumNodesPoint: Negative intergration order."); |
434 |
return -1; |
435 |
} else { |
436 |
return 0; |
437 |
} |
438 |
} |
439 |
|
440 |
int Finley_Quad_getNumNodesLine(int order) { |
441 |
char error_msg[LenErrorMsg_MAX]; |
442 |
if (order <0 ) { |
443 |
Finley_setError(VALUE_ERROR,"Finley_Quad_getNumNodesPoint: Negative intergration order."); |
444 |
return -1; |
445 |
} else { |
446 |
if (order > 2*MAX_numQuadNodesLine-1) { |
447 |
sprintf(error_msg,"Finley_Quad_getNumNodesPoint: requested integration order %d on line is too large (>%d).", |
448 |
order,2*MAX_numQuadNodesLine-1); |
449 |
Finley_setError(VALUE_ERROR,error_msg); |
450 |
return -1; |
451 |
} else { |
452 |
Finley_resetError(); |
453 |
return order/2+1; |
454 |
} |
455 |
} |
456 |
} |
457 |
|
458 |
int Finley_Quad_getNumNodesTri(int order) { |
459 |
int numQuadNodesLine; |
460 |
if (order==1) { |
461 |
return 1; |
462 |
} else { |
463 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+1); |
464 |
if (Finley_noError()) { |
465 |
return numQuadNodesLine*numQuadNodesLine; |
466 |
} else { |
467 |
return -1; |
468 |
} |
469 |
} |
470 |
} |
471 |
|
472 |
int Finley_Quad_getNumNodesRec(int order) { |
473 |
int numQuadNodesLine; |
474 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
475 |
if (Finley_noError()) { |
476 |
return numQuadNodesLine*numQuadNodesLine; |
477 |
} else { |
478 |
return -1; |
479 |
} |
480 |
} |
481 |
|
482 |
int Finley_Quad_getNumNodesTet(int order) { |
483 |
int numQuadNodesLine; |
484 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+2); |
485 |
if (Finley_noError()) { |
486 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
487 |
} else { |
488 |
return -1; |
489 |
} |
490 |
} |
491 |
|
492 |
int Finley_Quad_getNumNodesHex(int order) { |
493 |
int numQuadNodesLine; |
494 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
495 |
if (Finley_noError()) { |
496 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
497 |
} else { |
498 |
return -1; |
499 |
} |
500 |
} |
501 |
/* |
502 |
* $Log$ |
503 |
* Revision 1.2 2005/09/15 03:44:23 jgs |
504 |
* Merge of development branch dev-02 back to main trunk on 2005-09-15 |
505 |
* |
506 |
* Revision 1.1.1.1.6.1 2005/09/07 06:26:20 gross |
507 |
* the solver from finley are put into the standalone package paso now |
508 |
* |
509 |
* Revision 1.1.1.1 2004/10/26 06:53:57 jgs |
510 |
* initial import of project esys2 |
511 |
* |
512 |
* Revision 1.2 2004/08/03 04:49:06 gross |
513 |
* bug in Quadrature.c fixed |
514 |
* |
515 |
* Revision 1.1.1.1 2004/06/24 04:00:40 johng |
516 |
* Initial version of eys using boost-python. |
517 |
* |
518 |
* |
519 |
*/ |