DUNE PDELab (git)

blocksorpreconditioner.hh
1// -*- tab-width: 2; indent-tabs-mode: nil -*-
2// vi: set et ts=2 sw=2 sts=2:
3#ifndef DUNE_PDELAB_BACKEND_ISTL_MATRIXFREE_BLOCKSORPRECONDITIONER_HH
4#define DUNE_PDELAB_BACKEND_ISTL_MATRIXFREE_BLOCKSORPRECONDITIONER_HH
5
6namespace Dune {
7 namespace PDELab {
8
37 template<typename JacobianLOP, typename BlockOffDiagonalLOP, typename GridFunctionSpace>
41 {
42 using value_type = typename GridFunctionSpace::Traits::GridView::Grid::ctype;
45
46 public :
47 // A SOR preconditioner includes non-diagonal blocks so we need volume
48 // and skeleton methods. We do two-sided assembly!
49 static constexpr bool doPatternVolume = true;
50 static constexpr bool doPatternSkeleton = true;
51 static constexpr bool doPatternVolumePostSkeleton = true;
52 static constexpr bool doAlphaVolume = true;
53 static constexpr bool doAlphaSkeleton = true;
54 static constexpr bool doAlphaVolumePostSkeleton = true;
55 static constexpr bool doSkeletonTwoSided = true;
56 static constexpr bool isLinear = JacobianLOP::isLinear;
57
58 BlockSORPreconditionerLocalOperator(JacobianLOP& jacobianlop,
59 BlockOffDiagonalLOP& blockOffDiagonalLOP,
60 const GridFunctionSpace& gridFunctionSpace,
61 const double omega=1.0)
62 : _jacobianlop(jacobianlop)
63 , _blockOffDiagonalLOP(blockOffDiagonalLOP)
64 , _omega(omega)
65 , _a_i(gridFunctionSpace.ordering().maxLocalSize())
66 , _b_i(gridFunctionSpace.ordering().maxLocalSize())
67 {}
68
74 {
75 return _jacobianlop.requireSetup();
76 }
77 void setRequireSetup(bool v)
78 {
79 _jacobianlop.setRequireSetup(v);
80 }
81
83 template<typename EG, typename LFSU, typename X, typename LFSV, typename Y>
84 void alpha_volume(const EG& eg, const LFSU& lfsu, const X& x, const LFSV& lfsv, Y& y) const
85 {
86 _jacobianlop.alpha_volume(eg,lfsu,x,lfsv,y);
87 }
88
90 template<typename IG, typename LFSU, typename X, typename LFSV, typename Y>
91 void alpha_skeleton(const IG& ig,
92 const LFSU& lfsu_s, const X& x_s, const LFSV& lfsv_s,
93 const LFSU& lfsu_n, const X& x_n, const LFSV& lfsv_n,
94 Y& y_s, Y& y_n) const
95 {}
96
98 template<typename EG, typename LFSU, typename X, typename LFSV, typename Y>
99 void alpha_volume_post_skeleton(const EG& eg, const LFSU& lfsu, const X& x, const LFSV& lfsv, Y& y) const
100 {}
101
103 template<typename EG, typename LFSU, typename X, typename LFSV, typename Y>
104 void jacobian_apply_volume(const EG& eg,
105 const LFSU& lfsu, const X& x,
106 const LFSV& lfsv, Y& y) const
107 {
108 //====================================
109 // How does this preconditioner work
110 //====================================
111 //
112 // When jacobian_apply is called on the grid operator the assembly
113 // machine will iterate over the grid. Since we have set twosided to
114 // true the order of methods will be:
115 //
116 // jacobian_apply_volume
117 // jacobian_apply_skeleton for each intersection
118 // jacobian_apply_volume_post_skeleton
119 //
120 // In the volume part we set _a_i to zero. During the skeleton part we
121 // apply the off-diagonal blocks to the old and new solution, step (1)
122 // of the algorithm description at the top of this class. In the
123 // post_skeleton section we will do steps (2) and (3) of the algorithm.
124 _a_i = 0.0;
125 }
126
128 template<typename EG, typename LFSU, typename X, typename Z, typename LFSV, typename Y>
129 void jacobian_apply_volume(const EG& eg, const LFSU& lfsu, const X& x, const Z& z, const LFSV& lfsv, Y& y) const
130 {
131 _a_i = 0.0;
132 }
133
135 template<typename IG, typename LFSU, typename Z, typename LFSV, typename Y>
136 void jacobian_apply_skeleton(const IG& ig,
137 const LFSU& lfsu_s, const Z& z_s, const LFSV& lfsv_s,
138 const LFSU& lfsu_n, const Z& z_n, const LFSV& lfsv_n,
139 Y& y_s, Y& y_n) const
140 {
141 // This step is bit tricky.
142 //
143 // In the apply method of the GridOperatorPreconditioner class
144 // jacobian_apply(d, v) is called on the preconditioner grid
145 // operator.
146 //
147 // z_s and z_n will be the local entries of the block vector d.
148 //
149 // y_s will always be the solution of the previous step, e.i
150 // $v_i^{(k-1)} in the above algorithm. This will be zero since that is
151 // the value you get from ISTL for v^{(0)} and we do only one
152 // preconditioner step.
153 //
154 // For cells you have not yet visited y_n will also be the old solution
155 // $v_j^{(k-1)}. If you have already visited the neigbor cell it will
156 // instead be the new solution $v_j^{(k)}$.
157 //
158 // For this reason we pass the local vectors of y_s and y_n as
159 // coefficients to the block off-diagonal local operator. The result
160 // will be accumulated in _a_i. Following the above algorithm we will
161 // have
162 //
163 // _a_i = \sum_{j<i} A_ij v_j^{(k)} + \sum_{j>i} A_ij v_j^{(k-1)}
164 //
165 // after visiting all the intersections.
166 //
167 // NOTE: This only work for the FastDGGridOperator!
168 //
169 // This works perfectly for the FastDGGridOperator: The fast-DG
170 // grid operator directly works on the degrees of freedom vector, so if
171 // we set some values during the jacobian apply skeleton we will get
172 // the correct result in the jacobian apply post skeleton.
173 //
174 // For the regular GridOperator we instead write data into a local
175 // degrees of freedom vectors and the results will only written back to
176 // the global data structure during unbinding of the LFS. This means
177 // you get the same old coefficients in the
178 // jacobian_apply_volume_post_skeleton. There are two ways around this issue:
179 //
180 // 1. Copy data, e.g. by storing the values as members of this
181 // class. This does not require changing pdelab, but: Copying data is
182 // slow and the whole point of matrix-free solvers is to avoid
183 // unnecessary memory work. In the end all these solvers are intended
184 // to be used together with the FastDGGridOperator.
185 //
186 // 2. It would be possible to change the GridOperator assembler. This
187 // is not really appealing since it's behavior is perfect for the
188 // regular use case and having an additional unbind/bind would slow
189 // down those regular use cases.
190 //
191 // It is of course possible to achieve both: A fast implementation in
192 // case of FastDGGridOperator and a slower one for regular GridOperator
193 // involving data movement but this would make this whole
194 // implementation even more complicated without big benefits.
195 W _a_i_view(_a_i, y_s.weight());
196 if (ig.inside().partitionType() == Dune::InteriorEntity){
197 // Note: Since the block off diagonal local operator works two sided
198 // we can pass _a_i_view two times to the jacobian_apply_skeleton but
199 // will only accumulate once.
200
201 // TODO: Only works for FastDGGridOperator (y_* being an AliasedVectorView)
202 _blockOffDiagonalLOP.jacobian_apply_skeleton(ig, lfsu_s, y_s, lfsv_s, lfsu_n, y_n, lfsv_s, _a_i_view, _a_i_view);
203 }
204 }
205
207 template<typename IG, typename LFSU, typename X, typename Z, typename LFSV, typename Y>
208 void jacobian_apply_skeleton(const IG& ig,
209 const LFSU& lfsu_s, const X& x_s, const Z& z_s, const LFSV& lfsv_s,
210 const LFSU& lfsu_n, const X& x_n, const Z& z_n, const LFSV& lfsv_n,
211 Y& y_s, Y& y_n) const
212 {
213 // See documentation above!
214 W _a_i_view(_a_i, y_s.weight());
215 if (ig.inside().partitionType() == Dune::InteriorEntity)
216 _blockOffDiagonalLOP.jacobian_apply_skeleton(ig, lfsu_s, x_s, y_s, lfsv_s, lfsu_n, x_n, y_n, lfsv_s, _a_i_view, _a_i_view);
217 }
218
220 template<typename EG, typename LFSU, typename X, typename LFSV, typename Y>
222 const LFSU& lfsu, const X& x,
223 const LFSV& lfsv, Y& y) const
224 {
225 // Subtracting x: _a_i -= x_e. Looking at the algorithm above this
226 // finishes step (1) since the coefficient x is the vector d
227 // above. After this we have r_tmp = - a_i
228 std::transform(_a_i.data(),
229 _a_i.data() + _a_i.size(),
230 x.data(),
231 _a_i.data(),
232 std::minus<value_type>{});
233
234 // Solve the block diagonal system. This is step (2) of the
235 // algorithm. After this we have _b_i = -b_i.
236 _b_i = 0.0;
237 W _b_i_view(_b_i, y.weight());
238 _jacobianlop.jacobian_apply_volume(eg, lfsu, _a_i, lfsv, _b_i_view);
239
240
241 // Do the Update step (3) of the algorithm
242 std::transform(y.data(),
243 y.data() + y.size(),
244 _b_i.data(),
245 y.data(),
246 [this](const double &a,
247 const double& b)
248 {
249 return (1-_omega)*a - _omega*b;
250 });
251 }
252
254 template<typename EG, typename LFSU, typename X, typename Z, typename LFSV, typename Y>
255 void jacobian_apply_volume_post_skeleton(const EG& eg, const LFSU& lfsu, const X& x, const Z& z, const LFSV& lfsv, Y& y) const
256 {
257 // static checks
258 //----------------------
259 // static_assert(std::is_same<decltype(x),decltype(_a_i)>::value,"Both types have to be the same for nonlinear Jacobian apply");
260 // static_assert(not std::is_same<decltype(x),decltype(_a_i)>::value,"Both types have to be the same for nonlinear Jacobian apply");
261 //
262 // dynamic crashes
263 //----------------------
264 // x.bar(); // type ConstAliasedVectorView
265 // _a_i.bar(); // type LocalVector<double, >
266
267 // Subtract x_e: _a_i -= x_e
268 std::transform(_a_i.data(),_a_i.data()+_a_i.size(),
269 z.data(),
270 _a_i.data(),
271 std::minus<value_type>{});
272 // Divide by block diagonal, _b_i = D_{ee}^{-1} _a_i
273 _b_i = 0.0;
274 W _b_i_view(_b_i,y.weight());
275 _jacobianlop.jacobian_apply_volume(eg, lfsu, x, _a_i, lfsv, _b_i_view);
276 // Update vector r_e -= omega*_b_i
277 // <=> r_e = (1-\omega)r_e + \omega D_{ee}^{-1}(x_e - \sum_{e'}A_{e,e'}r_{e'})
278 std::transform(y.data(),
279 y.data()+y.size(),
280 _b_i.data(),
281 y.data(),
282 [this](const double& a,
283 const double& b)
284 {
285 return (1-_omega)*a - _omega*b;
286 });
287 }
288
289 private :
290
291 JacobianLOP& _jacobianlop;
292 BlockOffDiagonalLOP& _blockOffDiagonalLOP;
293 const double _omega;
294 mutable LocalVector _a_i;
295 mutable LocalVector _b_i;
296 }; // end class BlockSORPreconditionerLocalOperator
297
298 } // namespace PDELab
299} // namespace Dune
300
301#endif
Turn a matrix-free Jacobi-type local preconditioner to a SOR one.
Definition: blocksorpreconditioner.hh:41
void jacobian_apply_skeleton(const IG &ig, const LFSU &lfsu_s, const X &x_s, const Z &z_s, const LFSV &lfsv_s, const LFSU &lfsu_n, const X &x_n, const Z &z_n, const LFSV &lfsv_n, Y &y_s, Y &y_n) const
Gather off-block-diagonals in Gauss-Seidel process of linearized operator.
Definition: blocksorpreconditioner.hh:208
void jacobian_apply_volume_post_skeleton(const EG &eg, const LFSU &lfsu, const X &x, const Z &z, const LFSV &lfsv, Y &y) const
apply preconditioner after skeleton terms, linearized version
Definition: blocksorpreconditioner.hh:255
void alpha_volume(const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, Y &y) const
Prepare underlying diagonal block preconditioner.
Definition: blocksorpreconditioner.hh:84
void alpha_skeleton(const IG &ig, const LFSU &lfsu_s, const X &x_s, const LFSV &lfsv_s, const LFSU &lfsu_n, const X &x_n, const LFSV &lfsv_n, Y &y_s, Y &y_n) const
Provide this method, but it actually does not nothing.
Definition: blocksorpreconditioner.hh:91
bool requireSetup()
Definition: blocksorpreconditioner.hh:73
void jacobian_apply_volume_post_skeleton(const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, Y &y) const
Apply preconditioner after skeleton terms, linear version.
Definition: blocksorpreconditioner.hh:221
void jacobian_apply_volume(const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, Y &y) const
Linear operator application, volume terms.
Definition: blocksorpreconditioner.hh:104
void jacobian_apply_volume(const EG &eg, const LFSU &lfsu, const X &x, const Z &z, const LFSV &lfsv, Y &y) const
linearized operator application, volume terms
Definition: blocksorpreconditioner.hh:129
void alpha_volume_post_skeleton(const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, Y &y) const
Provide this method, but it actually does nothing.
Definition: blocksorpreconditioner.hh:99
void jacobian_apply_skeleton(const IG &ig, const LFSU &lfsu_s, const Z &z_s, const LFSV &lfsv_s, const LFSU &lfsu_n, const Z &z_n, const LFSV &lfsv_n, Y &y_s, Y &y_n) const
Gather off-block-diagonals in Gauss-Seidel process of linear operator.
Definition: blocksorpreconditioner.hh:136
sparsity pattern generator
Definition: pattern.hh:14
A grid function space.
Definition: gridfunctionspace.hh:191
Default flags for all local operators.
Definition: flags.hh:19
size_type size() const
The size of the container.
Definition: localvector.hh:318
WeightedVectorAccumulationView< LocalVector > WeightedAccumulationView
An accumulate-only view of this container that automatically applies a weight to all contributions.
Definition: localvector.hh:211
auto data()
Access underlying container.
Definition: localvector.hh:244
@ InteriorEntity
all interior entities
Definition: gridenums.hh:31
const Ordering & ordering() const
Direct access to the DOF ordering.
Definition: gridfunctionspace.hh:414
Dune namespace.
Definition: alignedallocator.hh:13
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