PoissonSolver3DCylindricalGPU adalah pustaka yang dikembangkan untuk menyelesaikan persamaan Poisson 3 dimensi dalam sistem koordinat silinder dengan akselerator GPU
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/// \class PoissonSolver3DCylindricalGPU
/// \brief Kelas ini merupakan interface PoissonSolver 3D dalam koordinat silindrikal
/// yang diterapkan pada NVDIA Cuda
///
///
///
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/// \author Rifki Sadikin <rifki.sadikin@lipi.go.id>, Indonesian Institute of Sciences
/// \date Nov 8, 2018
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#include <math.h>
#include "PoissonSolver3DCylindricalGPU.h"
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const float PoissonSolver3DCylindricalGPU::fgkZ0 = 249.7; ///< nominal gating grid position
const float PoissonSolver3DCylindricalGPU::fgkIFCRadius = 83.5; ///< radius which renders the "18 rod manifold" best -> compare calc. of Jim Thomas
const float PoissonSolver3DCylindricalGPU::fgkOFCRadius = 254.5; ///< Mean Radius of the Outer Field Cage (252.55 min, 256.45 max) (cm)
float PoissonSolver3DCylindricalGPU::fgExactErr = 1e-4;
float PoissonSolver3DCylindricalGPU::fgConvergenceError = 1e-3;
/// constructor
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///
PoissonSolver3DCylindricalGPU::PoissonSolver3DCylindricalGPU() {
fErrorConvF = new float [fMgParameters.nMGCycle];
fErrorExactF = new float [fMgParameters.nMGCycle];
}
PoissonSolver3DCylindricalGPU::PoissonSolver3DCylindricalGPU(int nRRow, int nZColumn, int nPhiSlice) {
fNRRow = nRRow;
fNZColumn = nZColumn;
fPhiSlice = nPhiSlice;
fErrorConvF = new float [fMgParameters.nMGCycle];
fErrorExactF = new float [fMgParameters.nMGCycle];
}
/// destructor
PoissonSolver3DCylindricalGPU::~PoissonSolver3DCylindricalGPU() {
delete fErrorConvF;
delete fErrorExactF;
delete fExactSolutionF;
}
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/// Menyediakan solusi iteratif terhadap poisson solver pada koordinat silindrikal 3D
///
/// Disediakan algoritma iteratif
/// * Geometric MultiGrid
/// * Cycles: V, W, Full
/// * Relaxation: Gauss-Seidel
/// * Grid transfer operators: Full, Half
///
/// \param matricesV float * potential dalam array 1D berukuran nRRow*nZColumn *phiSlice
/// \param matricesCharge float * charge dalam array 1D berukuran nRRow*nZColumn *phiSlice
/// \param nRRow int jumlah titik grid pada arah radial
/// \param nZColumn int jumlah titik grid pada arah z
/// \param phiSlice int jumlah titik grid pada arah sudut (phi)
/// \param maxIteration int jumlah iterasi maksimum pada multigrud
/// \param symmetry int nilai simetri (tidak dipakai)
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void PoissonSolver3DCylindricalGPU::PoissonSolver3D(float *matricesV, float *matricesCharge,
int nRRow, int nZColumn, int phiSlice, int maxIteration,
int symmetry) {
fNRRow = nRRow;
fNZColumn = nZColumn;
fPhiSlice = phiSlice;
PoissonMultiGrid3D2D(matricesV, matricesCharge, nRRow, nZColumn, phiSlice, symmetry);
}
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/// Penyelesaian Poisson problem dalam 3D Silindrikal dengan coarsening hanya pada arah z dan radial
///
/// Syarat:
/// R Row == 2**M + 1
/// Z Column == 2**N + 1
/// Phi Slice == Sembarang lebih besar > 3
///
/// Menyelesaikan: \f$ \nabla^{2}V(r,\phi,z) = - f(r,\phi,z) \f$
///
///
/// \param matricesV float * potential dalam array 1D berukuran nRRow*nZColumn *phiSlice
/// \param matricesCharge float * charge dalam array 1D berukuran nRRow*nZColumn *phiSlice
/// \param nRRow int jumlah titik grid pada arah radial
/// \param nZColumn int jumlah titik grid pada arah z
/// \param phiSlice int jumlah titik grid pada arah sudut (phi)
/// \param maxIteration int jumlah iterasi maksimum pada multigrud
/// \param symmetry int nilai simetri (tidak dipakai)
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void PoissonSolver3DCylindricalGPU::PoissonMultiGrid3D2D(float *VPotential, float * RhoChargeDensities, int nRRow,
int nZColumn, int phiSlice, int symmetry) {
const float gridSizeR = (PoissonSolver3DCylindricalGPU::fgkOFCRadius-PoissonSolver3DCylindricalGPU::fgkIFCRadius) / (nRRow-1); // h_{r}
const float gridSizePhi = M_PI/phiSlice; // h_{phi}
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const float gridSizeZ = PoissonSolver3DCylindricalGPU::fgkZ0 / (nZColumn-1) ; // h_{z}
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const float ratioPhi = gridSizeR*gridSizeR / (gridSizePhi*gridSizePhi) ; // ratio_{phi} = gridsize_{r} / gridsize_{phi}
const float ratioZ = gridSizeR*gridSizeR / (gridSizeZ*gridSizeZ) ; // ratio_{Z} = gridsize_{r} / gridsize_{z}
const float convErr = PoissonSolver3DCylindricalGPU::fgConvergenceError;
const float IFCRadius = PoissonSolver3DCylindricalGPU::fgkIFCRadius;
int fparamsize = 8;
float * fparam = new float[fparamsize];
fparam[0] = gridSizeR;
fparam[1] = gridSizePhi;
fparam[2] = gridSizeZ;
fparam[3] = ratioPhi;
fparam[4] = ratioZ;
fparam[5] = convErr;
fparam[6] = IFCRadius;
int iparamsize = 4;
int * iparam = new int[iparamsize];
iparam[0] = fMgParameters.nPre;
iparam[1] = fMgParameters.nPost;
iparam[2] = fMgParameters.maxLoop;
iparam[3] = fMgParameters.nMGCycle;
if (fMgParameters.cycleType == kFCycle)
{
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if (fExactPresent == true) {
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PoissonMultigrid3DSemiCoarseningGPUErrorFCycle(VPotential, RhoChargeDensities,nRRow, nZColumn,phiSlice,symmetry, fparam, iparam, fExactPresent, fErrorConvF, fErrorExactF, fExactSolutionF);
} else {
PoissonMultigrid3DSemiCoarseningGPUErrorFCycle(VPotential, RhoChargeDensities,nRRow, nZColumn,phiSlice,symmetry, fparam, iparam, fExactPresent, fErrorConvF, fErrorExactF, NULL);
}
} else if (fMgParameters.cycleType == kWCycle)
{
PoissonMultigrid3DSemiCoarseningGPUErrorWCycle(VPotential, RhoChargeDensities,nRRow, nZColumn,phiSlice,symmetry, fparam, iparam, fErrorConvF, fErrorExactF, fExactSolutionF);
} else
{
if (fExactPresent == true) {
PoissonMultigrid3DSemiCoarseningGPUError(VPotential, RhoChargeDensities,nRRow, nZColumn,phiSlice,symmetry, fparam, iparam, fExactPresent, fErrorConvF, fErrorExactF, fExactSolutionF);
} else {
PoissonMultigrid3DSemiCoarseningGPUError(VPotential, RhoChargeDensities,nRRow, nZColumn,phiSlice,symmetry, fparam, iparam, fExactPresent, fErrorConvF, fErrorExactF, NULL);
}
}
fIterations = iparam[3];
delete[] fparam;
delete[] iparam;
}
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/// Helper untuk menset nilai V dari fungsi analitik (diperlukan untuk memastikan implementasi benar
/// \param exactSolution float * array 1D sebesar nRRow * nZColumn * phiSlice
///
/// \param nRRow int jumlah titik grid pada arah radial
/// \param nZColumn int jumlah titik grid pada arah z
/// \param phiSlice int jumlah titik grid pada arah sudut (phi)
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void PoissonSolver3DCylindricalGPU::SetExactSolution(float*exactSolution,int nRRow, int nZColumn, int phiSlice) {
fNRRow = nRRow;
fNZColumn = nZColumn;
fPhiSlice = phiSlice;
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fExactSolutionF = new float[fNRRow * fPhiSlice * fNZColumn];
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fExactPresent = true;
fMaxExact = 0.0;;
for (int i=0;i<nRRow*nZColumn*phiSlice;i++) {
fExactSolutionF[i] = exactSolution[i];
if (abs(fExactSolutionF[i]) > fMaxExact) fMaxExact = abs(fExactSolutionF[i]);
}
}