StVKStiffnessMatrix::StVKStiffnessMatrix(StVKInternalForces * stVKInternalForces) { precomputedIntegrals = stVKInternalForces->GetPrecomputedIntegrals(); volumetricMesh = stVKInternalForces->GetVolumetricMesh(); numElementVertices = volumetricMesh->getNumElementVertices(); int numElements = volumetricMesh->getNumElements(); lambdaLame = (double*) malloc (sizeof(double) * numElements); muLame = (double*) malloc (sizeof(double) * numElements); for(int el=0; el<numElements; el++) { VolumetricMesh::Material * material = volumetricMesh->getElementMaterial(el); VolumetricMesh::ENuMaterial * eNuMaterial = downcastENuMaterial(material); if (eNuMaterial == NULL) { printf("Error: mesh does not consist of E, nu materials.\n"); throw 1; } lambdaLame[el] = eNuMaterial->getLambda(); muLame[el] = eNuMaterial->getMu(); } // build stiffness matrix skeleton SparseMatrix * stiffnessMatrixTopology; GetStiffnessMatrixTopology(&stiffnessMatrixTopology); // build acceleration indices row_ = (int**) malloc (sizeof(int*) * numElements); column_ = (int**) malloc (sizeof(int*) * numElements); for (int el=0; el < numElements; el++) { row_[el] = (int*) malloc (sizeof(int) * numElementVertices); column_[el] = (int*) malloc (sizeof(int) * numElementVertices * numElementVertices); for(int ver=0; ver<numElementVertices; ver++) row_[el][ver] = volumetricMesh->getVertexIndex(el, ver); // seek for value row[j] in list associated with row[i] for(int i=0; i<numElementVertices; i++) for(int j=0; j<numElementVertices; j++) column_[el][numElementVertices * i + j] = stiffnessMatrixTopology->GetInverseIndex(3*row_[el][i],3*row_[el][j]) / 3; } delete(stiffnessMatrixTopology); }
void IsotropicHyperelasticFEMMT::Initialize() { energyBuffer = (double*) malloc (sizeof(double) * numThreads); internalForceBuffer = (double*) malloc (sizeof(double) * numThreads * 3 * tetMesh->getNumVertices()); // generate skeleton matrices tangentStiffnessMatrixBuffer = (SparseMatrix**) malloc (sizeof(SparseMatrix*) * numThreads); SparseMatrix * sparseMatrix; GetStiffnessMatrixTopology(&sparseMatrix); for(int i=0; i<numThreads; i++) tangentStiffnessMatrixBuffer[i] = new SparseMatrix(*sparseMatrix); // split the workload int numElements = tetMesh->getNumElements(); startElement = (int*) malloc (sizeof(int) * numThreads); endElement = (int*) malloc (sizeof(int) * numThreads); int remainder = numElements % numThreads; // the first 'remainder' nodes will process one edge more int jobSize = numElements / numThreads; for(int rank=0; rank < numThreads; rank++) { if (rank < remainder) { startElement[rank] = rank * (jobSize+1); endElement[rank] = (rank+1) * (jobSize+1); } else { startElement[rank] = remainder * (jobSize+1) + (rank-remainder) * jobSize; endElement[rank] = remainder * (jobSize+1) + ((rank-remainder)+1) * jobSize; } } printf("Total elements: %d \n", numElements); printf("Num threads: %d \n", numThreads); printf("Canonical job size: %d \n", jobSize); printf("Num threads with job size augmented by one edge: %d \n", remainder); }
CorotationalLinearFEM::CorotationalLinearFEM(TetMesh * tetMesh_) : tetMesh(tetMesh_) { numVertices = tetMesh->getNumVertices(); // store the undeformed positions undeformedPositions = (double*) malloc (sizeof(double) * 3 * numVertices); for(int i=0; i < numVertices; i++) { Vec3d * v = tetMesh->getVertex(i); for(int j=0; j<3; j++) undeformedPositions[3*i+j] = (*v)[j]; } int numElements = tetMesh->getNumElements(); MInverse = (double**) malloc (sizeof(double*) * numElements); for(int el = 0; el < numElements; el++) { // get the integer indices of the tet vertices int vtxIndex[4]; for(int vtx=0; vtx<4; vtx++) vtxIndex[vtx] = tetMesh->getVertexIndex(el, vtx); /* Form matrix: M = [ v0 v1 v2 v3 ] [ 1 1 1 1 ] */ double M[16]; // row-major for(int vtx=0; vtx<4; vtx++) for(int dim=0; dim<3; dim++) M[4 * dim + vtx] = undeformedPositions[3 * vtxIndex[vtx] + dim]; M[12] = M[13] = M[14] = M[15] = 1.0; // invert M and cache inverse (see [Mueller 2004]) MInverse[el] = (double*) malloc (sizeof(double) * 16); inverse4x4(M, MInverse[el]); } // build acceleration indices for fast writing to the global stiffness matrix SparseMatrix * sparseMatrix; GetStiffnessMatrixTopology(&sparseMatrix); BuildRowColumnIndices(sparseMatrix); delete(sparseMatrix); // compute stiffness matrices for all the elements in the undeformed configuration KElementUndeformed = (double**) malloc (sizeof(double*) * numElements); for (int el = 0; el < numElements; el++) { double * MInv = MInverse[el]; // Form stiffness matrix of the element in the undeformed configuration. // The procedure below is standard in FEM solid mechanics. // This code implements the equations given in Ahmed A. Shabana: Theory of Vibration, Volume II: Discrete and Continuous Systems, Springer--Verlag, New York, NY, 1990. double B[72] = { MInv[0], 0, 0, MInv[4], 0, 0, MInv[8], 0, 0, MInv[12], 0, 0, 0, MInv[1], 0, 0, MInv[5], 0, 0, MInv[9], 0, 0, MInv[13], 0, 0, 0, MInv[2], 0, 0, MInv[6], 0, 0, MInv[10], 0, 0, MInv[14], MInv[1], MInv[0], 0, MInv[5], MInv[4], 0, MInv[9], MInv[8], 0, MInv[13], MInv[12], 0, 0, MInv[2], MInv[1], 0, MInv[6], MInv[5], 0, MInv[10], MInv[9], 0, MInv[14], MInv[13], MInv[2], 0, MInv[0], MInv[6], 0, MInv[4], MInv[10], 0, MInv[8], MInv[14], 0, MInv[12] }; // compute elasticity stiffness tensor double E[36]; // 6 x 6 matrix, stored row-major (symmetric, so row vs column-major storage makes no difference anyway) VolumetricMesh::Material * material = tetMesh->getElementMaterial(el); // check if material is ENuMaterial (i.e., isotropic) VolumetricMesh::ENuMaterial * eNuMaterial = downcastENuMaterial(material); if (eNuMaterial != NULL) { // material is isotropic, specified by E, nu // compute Lame coefficients double lambda = eNuMaterial->getLambda(); double mu = eNuMaterial->getMu(); double Et[36] = { lambda + 2 * mu, lambda, lambda, 0, 0, 0, lambda, lambda + 2 * mu, lambda, 0, 0, 0, lambda, lambda, lambda + 2 * mu, 0, 0, 0, 0, 0, 0, mu, 0, 0, 0, 0, 0, 0, mu, 0, 0, 0, 0, 0, 0, mu }; memcpy(E, Et, sizeof(double) * 36); } else { // orthotropic material // we follow the following references: // Yijing Li and Jernej Barbic: Stable Orthotropic Materials, Symposium on Computer Animation 2014 // http://en.wikipedia.org/wiki/Orthotropic_material // http://www.solidmechanics.org/text/Chapter3_2/Chapter3_2.htm // test if material is OrthotropicMaterial (i.e., orthotropic) VolumetricMesh::OrthotropicMaterial * orthotropicMaterial = downcastOrthotropicMaterial(material); if (orthotropicMaterial != NULL) { double E1 = orthotropicMaterial->getE1(); double E2 = orthotropicMaterial->getE2(); double E3 = orthotropicMaterial->getE3(); double nu12 = orthotropicMaterial->getNu12(); double nu23 = orthotropicMaterial->getNu23(); double nu31 = orthotropicMaterial->getNu31(); double G12 = orthotropicMaterial->getG12(); double G23 = orthotropicMaterial->getG23(); double G31 = orthotropicMaterial->getG31(); double nu21 = nu12 * E2 / E1; double nu32 = nu23 * E3 / E2; double nu13 = nu31 * E1 / E3; double Y = 1.0 / (1.0 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 - 2.0 * nu21 * nu32 * nu13); double ELocal[36] = { E1 * (1.0 - nu23 * nu32) * Y, E1 * (nu21 + nu31 * nu23) * Y, E1 * (nu31 + nu21 * nu32) * Y, 0.0, 0.0, 0.0, E1 * (nu21 + nu31 * nu23) * Y, E2 * (1.0 - nu13 * nu31) * Y, E2 * (nu32 + nu12 * nu31) * Y, 0.0, 0.0, 0.0, E1 * (nu31 + nu21 * nu32) * Y, E2 * (nu32 + nu12 * nu31) * Y, E3 * (1.0 - nu12 * nu21) * Y, 0.0, 0.0, 0.0, 0, 0, 0, G12, 0, 0, 0, 0, 0, 0, G23, 0, 0, 0, 0, 0, 0, G31 }; //memcpy(E, ELocal, sizeof(double) * 36); // debug double R[9]; // row-major orthotropicMaterial->getR(R); // rotate Elocal into the basis given by the columns of R #define Relt(i,j) (R[3*(i)+(j)]) double rotator[36]; for(int i=0; i<3; i++) for(int j=0; j<3; j++) { rotator[6 * i + j] = Relt(i,j) * Relt(i,j); rotator[6 * i + 3 + j] = 2.0 * Relt(i, j) * Relt(i, (j+1) % 3); rotator[6 * (i + 3) + j] = Relt(i, j) * Relt((i+1) % 3, j); rotator[6 * (i + 3) + 3 + j] = Relt(i, j) * Relt((i+1) % 3, (j+1) % 3) + Relt(i, (j+1) % 3) * Relt((i+1) % 3, j); } #undef Relt // debug //memset(rotator, 0, sizeof(double) * 36); //for(int i=0; i<6; i++) //rotator[6*i+i] = 1.0; // E = rotator * ELocal * rotator^T double buffer[36]; memset(buffer, 0, sizeof(double) * 36); // buffer = ELocal * rotator^T for(int i=0; i<6; i++) for(int j=0; j<6; j++) for(int k=0; k<6; k++) buffer[6 * i + j] += ELocal[6 * i + k] * rotator[6 * j + k]; // E = rotator * buffer memset(E, 0, sizeof(double) * 36); for(int i=0; i<6; i++) for(int j=0; j<6; j++) for(int k=0; k<6; k++) E[6 * i + j] += rotator[6 * i + k] * buffer[6 * k + j]; } else { printf("Error: CorotationalLinearFEM: unknown material encounted in the mesh.\n"); throw 1; } } // EB = E * B double EB[72]; memset(EB, 0, sizeof(double) * 72); for (int i=0; i<6; i++) for (int j=0; j<12; j++) for (int k=0; k<6; k++) EB[12 * i + j] += E[6 * i + k] * B[12 * k + j]; // KElementUndeformed[el] = B^T * EB KElementUndeformed[el] = (double*) calloc (144, sizeof(double)); // element stiffness matrix for (int i=0; i<12; i++) for (int j=0; j<12; j++) for (int k=0; k<6; k++) KElementUndeformed[el][12 * i + j] += B[12 * k + i] * EB[12 * k + j]; // KElementUndeformed[el] *= volume double volume = TetMesh::getTetVolume(tetMesh->getVertex(el,0), tetMesh->getVertex(el,1), tetMesh->getVertex(el,2), tetMesh->getVertex(el,3)); for(int i=0; i<144; i++) KElementUndeformed[el][i] *= volume; } }