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/* |
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****************************************************************************** |
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* * |
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* COPYRIGHT ACcESS 2003,2004,2005 - All Rights Reserved * |
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* * |
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* This software is the property of ACcESS. No part of this code * |
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* may be copied in any form or by any means without the expressed written * |
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* consent of ACcESS. Copying, use or modification of this software * |
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* by any unauthorised person is illegal unless that person has a software * |
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* license agreement with ACcESS. * |
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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[numQuadNodes],quadWeights1d[numQuadNodes]; |
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#define DIM 2 |
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|
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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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} |
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return; |
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} |
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} |
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sprintf(error_msg,"__FILE__: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
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Finley_setError(VALUE_ERROR,error_msg); |
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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 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[numQuadNodes],quadWeights1d[numQuadNodes]; |
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#define DIM 3 |
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|
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/* find numQuadNodes1d with numQuadNodes1d**3==numQuadNodes: */ |
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|
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for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) { |
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if (numQuadNodes1d*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 3D scheme: */ |
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|
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if (Finley_noError()) { |
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l=0; |
| 182 |
for (i=0;i<numQuadNodes1d;i++) { |
| 183 |
for (j=0;j<numQuadNodes1d;j++) { |
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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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} |
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|
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return; |
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} |
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} |
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sprintf(error_msg,"__FILE__: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
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Finley_setError(VALUE_ERROR,error_msg); |
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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 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. */ |
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|
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void Finley_Quad_getNodesPoint(int numQuadNodes,double* quadNodes,double* quadWeights) { |
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if (numQuadNodes!=0) { |
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Finley_setError(VALUE_ERROR,"__FILE__: There is no quadrature scheme on points."); |
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} |
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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 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) { |
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switch(numQuadNodes) { |
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case 1: |
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quadNodes[0]=0.5; |
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quadWeights[0]=1.; |
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break; |
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|
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case 2: |
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quadNodes[0]=(1.-.577350269189626)/2.; |
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quadNodes[1]=(1.+.577350269189626)/2.; |
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quadWeights[0]=.5; |
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quadWeights[1]=.5; |
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break; |
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|
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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.; |
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quadWeights[2]=5./18.; |
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break; |
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|
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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.; |
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quadWeights[2]=.652145154862546/2.; |
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quadWeights[3]=.347854845137454/2.; |
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break; |
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|
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case 5: |
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quadNodes[0]=(1.-.906179845938664)/2.; |
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quadNodes[1]=(1.-.538469310105683)/2.; |
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quadNodes[2]= .5; |
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quadNodes[3]=(1.+.538469310105683)/2.; |
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quadNodes[4]=(1.+.906179845938664)/2.; |
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quadWeights[0]=.236926885056189/2.; |
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quadWeights[1]=.478628670499366/2.; |
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quadWeights[2]=.568888888888889/2.; |
| 263 |
quadWeights[3]=.478628670499366/2.; |
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quadWeights[4]=.236926885056189/2.; |
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break; |
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|
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case 6: |
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quadNodes[0]=(1.-.932469514203152)/2.; |
| 269 |
quadNodes[1]=(1.-.661209386466265)/2.; |
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quadNodes[2]=(1.-.238619186083197)/2.; |
| 271 |
quadNodes[3]=(1.+.238619186083197)/2.; |
| 272 |
quadNodes[4]=(1.+.661209386466265)/2.; |
| 273 |
quadNodes[5]=(1.+.932469514203152)/2.; |
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quadWeights[0]=.171324492379170/2.; |
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quadWeights[1]=.360761573048139/2.; |
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quadWeights[2]=.467913934572691/2.; |
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quadWeights[3]=.467913934572691/2.; |
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quadWeights[4]=.360761573048139/2.; |
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quadWeights[5]=.171324492379170/2.; |
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break; |
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|
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case 7: |
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quadNodes[0]=(1.-.949107912342759)/2.; |
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quadNodes[1]=(1.-.741531185599394)/2.; |
| 285 |
quadNodes[2]=(1.-.405845151377397)/2.; |
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quadNodes[3]=0.5; |
| 287 |
quadNodes[4]=(1.+.405845151377397)/2.; |
| 288 |
quadNodes[5]=(1.+.741531185599394)/2.; |
| 289 |
quadNodes[6]=(1.+.949107912342759)/2.; |
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quadWeights[0]= .129484966168870/2.; |
| 291 |
quadWeights[1]= .279705391489277/2.; |
| 292 |
quadWeights[2]= .381830050505119/2.; |
| 293 |
quadWeights[3]= .417959183673469/2.; |
| 294 |
quadWeights[4]= .381830050505119/2.; |
| 295 |
quadWeights[5]= .279705391489277/2.; |
| 296 |
quadWeights[6]= .129484966168870/2.; |
| 297 |
break; |
| 298 |
|
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case 8: |
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quadNodes[0]=(1.-.960289856497536)/2.; |
| 301 |
quadNodes[1]=(1.-.796666477413627)/2.; |
| 302 |
quadNodes[2]=(1.-.525532409916329)/2.; |
| 303 |
quadNodes[3]=(1.-.183434642495650)/2.; |
| 304 |
quadNodes[4]=(1.+.183434642495650)/2.; |
| 305 |
quadNodes[5]=(1.+.525532409916329)/2.; |
| 306 |
quadNodes[6]=(1.+.796666477413627)/2.; |
| 307 |
quadNodes[7]=(1.+.960289856497536)/2.; |
| 308 |
quadWeights[0]= .101228536290376/2.; |
| 309 |
quadWeights[1]= .222381034453374/2.; |
| 310 |
quadWeights[2]= .313706645877887/2.; |
| 311 |
quadWeights[3]= .362683783378362/2.; |
| 312 |
quadWeights[4]= .362683783378362/2.; |
| 313 |
quadWeights[5]= .313706645877887/2.; |
| 314 |
quadWeights[6]= .222381034453374/2.; |
| 315 |
quadWeights[7]= .101228536290376/2.; |
| 316 |
break; |
| 317 |
|
| 318 |
case 9: |
| 319 |
quadNodes[0]=(1.-.968160239507626)/2.; |
| 320 |
quadNodes[1]=(1.-.836031107326636)/2.; |
| 321 |
quadNodes[2]=(1.-.613371432700590)/2.; |
| 322 |
quadNodes[3]=(1.-.324253423403809)/2.; |
| 323 |
quadNodes[4]= .5; |
| 324 |
quadNodes[5]=(1.+.324253423403809)/2.; |
| 325 |
quadNodes[6]=(1.+.613371432700590)/2.; |
| 326 |
quadNodes[7]=(1.+.836031107326636)/2.; |
| 327 |
quadNodes[8]=(1.+.968160239507626)/2.; |
| 328 |
quadWeights[0]= .081274388361574/2.; |
| 329 |
quadWeights[1]= .180648160694857/2.; |
| 330 |
quadWeights[2]= .260610696402935/2.; |
| 331 |
quadWeights[3]= .312347077040003/2.; |
| 332 |
quadWeights[4]= .330239355001260/2.; |
| 333 |
quadWeights[5]= .312347077040003/2.; |
| 334 |
quadWeights[6]= .260610696402935/2.; |
| 335 |
quadWeights[7]= .180648160694857/2.; |
| 336 |
quadWeights[8]= .081274388361574/2.; |
| 337 |
break; |
| 338 |
|
| 339 |
case 10: |
| 340 |
quadNodes[0]=(1.-.973906528517172)/2.; |
| 341 |
quadNodes[1]=(1.-.865063366688985)/2.; |
| 342 |
quadNodes[2]=(1.-.679409568299024)/2.; |
| 343 |
quadNodes[3]=(1.-.433395394129247)/2.; |
| 344 |
quadNodes[4]=(1.-.148874338981631)/2.; |
| 345 |
quadNodes[5]=(1.+.148874338981631)/2.; |
| 346 |
quadNodes[6]=(1.+.433395394129247)/2.; |
| 347 |
quadNodes[7]=(1.+.679409568299024)/2.; |
| 348 |
quadNodes[8]=(1.+.865063366688985)/2.; |
| 349 |
quadNodes[9]=(1.+.973906528517172)/2.; |
| 350 |
quadWeights[0]= .066671344308688/2.; |
| 351 |
quadWeights[1]= .149451349150581/2.; |
| 352 |
quadWeights[2]= .219086362515982/2.; |
| 353 |
quadWeights[3]= .269266719309996/2.; |
| 354 |
quadWeights[4]= .295524224714753/2.; |
| 355 |
quadWeights[5]= .295524224714753/2.; |
| 356 |
quadWeights[6]= .269266719309996/2.; |
| 357 |
quadWeights[7]= .219086362515982/2.; |
| 358 |
quadWeights[8]= .149451349150581/2.; |
| 359 |
quadWeights[9]= .066671344308688/2.; |
| 360 |
break; |
| 361 |
|
| 362 |
default: |
| 363 |
Finley_setError(VALUE_ERROR,"__FILE__: Negative intergration order."); |
| 364 |
break; |
| 365 |
} |
| 366 |
} |
| 367 |
/**************************************************************/ |
| 368 |
/* */ |
| 369 |
/* the following function are used define the meshes on the surface in the xy-plane */ |
| 370 |
|
| 371 |
/* triangle surface on a tetrahedron */ |
| 372 |
void Finley_Quad_getNodesTriOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 373 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesTri); |
| 374 |
} |
| 375 |
/* rectangular surface on a hexahedron */ |
| 376 |
void Finley_Quad_getNodesRecOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 377 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesRec); |
| 378 |
} |
| 379 |
/* line surface on a triangle or rectangle */ |
| 380 |
void Finley_Quad_getNodesLineOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 381 |
Finley_Quad_makeNodesOnFace(2,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesLine); |
| 382 |
} |
| 383 |
/* point surface on a line */ |
| 384 |
void Finley_Quad_getNodesPointOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
| 385 |
Finley_Quad_makeNodesOnFace(1,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesPoint); |
| 386 |
} |
| 387 |
|
| 388 |
void Finley_Quad_makeNodesOnFace(int dim, int numQuadNodes,double* quadNodes,double* quadWeights, Finley_Quad_getNodes getFaceNodes) { |
| 389 |
int q,i; |
| 390 |
double quadNodesOnFace[numQuadNodes*(dim-1)]; |
| 391 |
|
| 392 |
#define DIM dim |
| 393 |
getFaceNodes(numQuadNodes,quadNodesOnFace,quadWeights); |
| 394 |
if (! Finley_noError()) return; |
| 395 |
|
| 396 |
for (q=0;q<numQuadNodes;q++) { |
| 397 |
for (i=0;i<dim-1;i++) QUADNODES(i,q)=quadNodesOnFace[INDEX2(i,q,dim-1)]; |
| 398 |
QUADNODES(dim-1,q)=0; |
| 399 |
} |
| 400 |
#undef DIM |
| 401 |
} |
| 402 |
|
| 403 |
/**************************************************************/ |
| 404 |
|
| 405 |
/* The following functions Finley_Quad_getNumNodes* return the nmber of quadrature points needed to */ |
| 406 |
/* achieve a certain accuracy. Notice that for Tet and Tri the the order is increased */ |
| 407 |
/* to consider the accuracy reduction through the construction process. */ |
| 408 |
|
| 409 |
|
| 410 |
int Finley_Quad_getNumNodesPoint(int order) { |
| 411 |
if (order <0 ) { |
| 412 |
Finley_setError(VALUE_ERROR,"__FILE__: Negative intergration order."); |
| 413 |
return -1; |
| 414 |
} else { |
| 415 |
return 0; |
| 416 |
} |
| 417 |
} |
| 418 |
|
| 419 |
int Finley_Quad_getNumNodesLine(int order) { |
| 420 |
char error_msg[LenErrorMsg_MAX]; |
| 421 |
if (order <0 ) { |
| 422 |
Finley_setError(VALUE_ERROR,"__FILE__: Negative intergration order."); |
| 423 |
return -1; |
| 424 |
} else { |
| 425 |
if (order > 2*MAX_numQuadNodesLine-1) { |
| 426 |
sprintf(error_msg,"__FILE__: requested integration order %d on line is too large (>%d).", |
| 427 |
order,2*MAX_numQuadNodesLine-1); |
| 428 |
Finley_setError(VALUE_ERROR,error_msg); |
| 429 |
return -1; |
| 430 |
} else { |
| 431 |
Finley_resetError(); |
| 432 |
return order/2+1; |
| 433 |
} |
| 434 |
} |
| 435 |
} |
| 436 |
|
| 437 |
int Finley_Quad_getNumNodesTri(int order) { |
| 438 |
int numQuadNodesLine; |
| 439 |
if (order==1) { |
| 440 |
return 1; |
| 441 |
} else { |
| 442 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+1); |
| 443 |
if (Finley_noError()) { |
| 444 |
return numQuadNodesLine*numQuadNodesLine; |
| 445 |
} else { |
| 446 |
return -1; |
| 447 |
} |
| 448 |
} |
| 449 |
} |
| 450 |
|
| 451 |
int Finley_Quad_getNumNodesRec(int order) { |
| 452 |
int numQuadNodesLine; |
| 453 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
| 454 |
if (Finley_noError()) { |
| 455 |
return numQuadNodesLine*numQuadNodesLine; |
| 456 |
} else { |
| 457 |
return -1; |
| 458 |
} |
| 459 |
} |
| 460 |
|
| 461 |
int Finley_Quad_getNumNodesTet(int order) { |
| 462 |
int numQuadNodesLine; |
| 463 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+2); |
| 464 |
if (Finley_noError()) { |
| 465 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
| 466 |
} else { |
| 467 |
return -1; |
| 468 |
} |
| 469 |
} |
| 470 |
|
| 471 |
int Finley_Quad_getNumNodesHex(int order) { |
| 472 |
int numQuadNodesLine; |
| 473 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
| 474 |
if (Finley_noError()) { |
| 475 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
| 476 |
} else { |
| 477 |
return -1; |
| 478 |
} |
| 479 |
} |
| 480 |
/* |
| 481 |
* $Log$ |
| 482 |
* Revision 1.2 2005/09/15 03:44:23 jgs |
| 483 |
* Merge of development branch dev-02 back to main trunk on 2005-09-15 |
| 484 |
* |
| 485 |
* Revision 1.1.1.1.6.1 2005/09/07 06:26:20 gross |
| 486 |
* the solver from finley are put into the standalone package paso now |
| 487 |
* |
| 488 |
* Revision 1.1.1.1 2004/10/26 06:53:57 jgs |
| 489 |
* initial import of project esys2 |
| 490 |
* |
| 491 |
* Revision 1.2 2004/08/03 04:49:06 gross |
| 492 |
* bug in Quadrature.c fixed |
| 493 |
* |
| 494 |
* Revision 1.1.1.1 2004/06/24 04:00:40 johng |
| 495 |
* Initial version of eys using boost-python. |
| 496 |
* |
| 497 |
* |
| 498 |
*/ |
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