| 1 | /**
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| 2 | * @file discretization_poisson_fd_collatz.hpp
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| 3 | * @author Julian Iseringhausen <isering@ins.uni-bonn.de>
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| 4 | * @date Mon Apr 18 13:02:26 2011
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| 5 | *
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| 6 | * @brief Collatz finite difference discretization of the
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| 7 | * Poisson equation for a higher order discretization
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| 8 | * while preserving compactness of the stencil.
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| 9 | *
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| 10 | */
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| 11 |
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| 12 |
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| 13 | #ifndef DISCRETIZATION_POISSON_FD_COLLATZ_HPP_
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| 14 | #define DISCRETIZATION_POISSON_FD_COLLATZ_HPP_
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| 15 |
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| 16 | #include "base/discretization.hpp"
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| 17 |
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| 18 | namespace VMG
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| 19 | {
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| 20 |
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| 21 | static inline vmg_float sqr(const vmg_float& val) {return val*val;}
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| 22 |
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| 23 | class DiscretizationPoissonFDCollatz : public Discretization
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| 24 | {
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| 25 | public:
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| 26 | DiscretizationPoissonFDCollatz()
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| 27 | {
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| 28 | stencil.SetDiag(24.0/6.0);
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| 29 |
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| 30 | stencil.push_back(Displacement(-1, 0, 0, -2.0/6.0));
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| 31 | stencil.push_back(Displacement( 1, 0, 0, -2.0/6.0));
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| 32 | stencil.push_back(Displacement( 0, -1, 0, -2.0/6.0));
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| 33 | stencil.push_back(Displacement( 0, 1, 0, -2.0/6.0));
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| 34 | stencil.push_back(Displacement( 0, 0, -1, -2.0/6.0));
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| 35 | stencil.push_back(Displacement( 0, 0, 1, -2.0/6.0));
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| 36 |
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| 37 | stencil.push_back(Displacement(-1, -1, 0, -1.0/6.0));
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| 38 | stencil.push_back(Displacement(-1, 1, 0, -1.0/6.0));
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| 39 | stencil.push_back(Displacement( 1, -1, 0, -1.0/6.0));
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| 40 | stencil.push_back(Displacement( 1, 1, 0, -1.0/6.0));
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| 41 | stencil.push_back(Displacement(-1, 0, -1, -1.0/6.0));
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| 42 | stencil.push_back(Displacement(-1, 0, 1, -1.0/6.0));
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| 43 | stencil.push_back(Displacement( 1, 0, -1, -1.0/6.0));
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| 44 | stencil.push_back(Displacement( 1, 0, 1, -1.0/6.0));
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| 45 | stencil.push_back(Displacement( 0, -1, -1, -1.0/6.0));
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| 46 | stencil.push_back(Displacement( 0, -1, 1, -1.0/6.0));
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| 47 | stencil.push_back(Displacement( 0, 1, -1, -1.0/6.0));
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| 48 | stencil.push_back(Displacement( 0, 1, 1, -1.0/6.0));
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| 49 | }
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| 50 |
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| 51 | vmg_float OperatorPrefactor(const Multigrid& grid) const
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| 52 | {
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| 53 | return 1.0 / (sqr(grid.MeshWidth()));
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| 54 | }
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| 55 |
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| 56 | private:
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| 57 | void SetInnerBoundaryCompute(Multigrid& grid) const {}
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| 58 | };
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| 59 |
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| 60 | class StencilPoissonCollatzRhs : public Stencil
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| 61 | {
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| 62 | public:
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| 63 | StencilPoissonCollatzRhs() : Stencil(0.5)
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| 64 | {
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| 65 | this->push_back(Displacement(-1, 0, 0, 1.0/12.0));
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| 66 | this->push_back(Displacement( 1, 0, 0, 1.0/12.0));
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| 67 | this->push_back(Displacement( 0, -1, 0, 1.0/12.0));
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| 68 | this->push_back(Displacement( 0, 1, 0, 1.0/12.0));
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| 69 | this->push_back(Displacement( 0, 0, -1, 1.0/12.0));
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| 70 | this->push_back(Displacement( 0, 0, 1, 1.0/12.0));
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| 71 | }
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| 72 | };
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| 73 |
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| 74 | }
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| 75 |
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| 76 | #endif /* DISCRETIZATION_POISSON_FD_HPP_ */
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