Files | |
| file | whb.h |
| Class Whb: stabilized hierarchical basis library. | |
Classes | |
| struct | sHBmat |
| struct HBmat Definition More... | |
Typedefs | |
| typedef struct sHBmat | HBmat |
| Declaration of the HBmat class as the HBmat structure. | |
Functions | |
| void | HBmat_initG (HBmat *thee, Bmat *Ppro, Bmat *Mlink, int meth) |
| Assembles the change of basis matrices for the HB Vcycle. | |
| void | HBmat_initA (HBmat *Ahb, HBmat *Ghb, Bmat *Alink) |
| Assembles the hierarchical matrix for the HB Vcycle. | |
| void | HBmat_killStructure (HBmat *thee) |
| Kills a chain of HBmat pointers. | |
| void | HBmat_initMulti (HBmat **Ahb, HBmat **Ghb, Bmat *A, Bmat *M, Bmat *Ppro, int meth) |
| Assembles the hierarchical matrix structures for the HB Vcycle. | |
| void | HBmat_killMulti (HBmat **Ahb, HBmat **Ghb) |
| Destruct the hierarchical structures. | |
| HBmat * | HBmat_ctor (Vmem *vmem, const char *bname, int pnumB) |
| The HBmat constructor. | |
| void | HBmat_dtor (HBmat **thee) |
| The HBmat destructor. | |
| void | HBmat_printSp (HBmat *thee, char *fname, int pflag) |
| Print an HBmat in MATLAB sparse form. | |
| void | HBmat_GHB2WMHB (HBmat *thee, Bmat *M) |
| Constructs G12/G22 for WMHB using Mhb and G21. | |
| HBmat* HBmat_ctor | ( | Vmem * | vmem, | |
| const char * | bname, | |||
| int | pnumB | |||
| ) |
The HBmat constructor.
| vmem | Memory management object | |
| bname | character string name for the matrix | |
| pnumB | num vector blocks |
| void HBmat_dtor | ( | HBmat ** | thee | ) |
The HBmat destructor.
| thee | Pointer to the HBmat object |
Constructs G12/G22 for WMHB using Mhb and G21.
* Notes: This routine is the second step in the construction of the * change of basis matrix for WMHB. It constructs the G12 and * G22 blocks using the mass matrix in the HB basis: * * [ G11 ] = [ 0 ] ; [ G12 ] = [ I ] inv(-Mhb_11) Mhb_12 * [ G21 ] [ R ] [ G22 ] [ R ] * * where Mhb is the previously formed mass matrix in the HB basis: * * Mhb = [ Mhb_11 Mhb_12 ] = [ I R'] [ M_11 M_12 ] [ I 0 ] * [ Mhb_21 Mhb_22 ] [ 0 I ] [ M_21 M_22 ] [ R I ] * * Here inv( . ) represents any approximation to the inverse. * To keep optimal complexity this should be chosen very carefully. * Some possible choices include special matrix polynomials, * mass lumping, or simply the inverse of the diagonal. * * The G12 and G22 blocks should be passed in with NULL_STATE * subblocks, with only their shape determined (i.e. just after * ctor). The G21 block must already exist, and contain the tail * of the prolongation matrix, i.e. P = [I ; R]. *
| thee | Pointer to the HBmat object | |
| M | Pointer to the Bmat object |
Assembles the hierarchical matrix for the HB Vcycle.
* Notes: This routine takes a pointer to an HBmat array, and * returns a linked (hierarchical) chain of fully assembled * HBmat's. Each of the links contains several block matrices, * which correspond to the stabilized subsections of the global * block (stiffness) matrix. All together, these stabilized * blocks form the entire stiffness matrix, with respect to the * recursively defined "hierarchical basis". * * Basic Inputs: * * HBmat *G change of basis matrices for each level * BXLN *A nodal stiffness matrix in doubly linked format * int minLev coarsest level in the hierarchy * * Basic Outputs (inside the HBmat chain): * * Bmat *A21, *A22, *A12 stabilized Mat blocks on each level *
| Ahb | nodal stiffness matrix in doubly linked format | |
| Ghb | change of basis matrices for each level | |
| Alink | coarsest level in the hierarchy |
Assembles the change of basis matrices for the HB Vcycle.
* Notes: This routine takes a pointer to an HBmat array, and * returns a linked (hierarchical) chain of fully assembled * HBmat's. Each of the links contains several block matrices, * which correspond to the logical subsections of the change * of basis matrix: * * [ S11 S12 ] = [ I 0 ] + [ G11 G12 ] * [ S21 S22 ] [ 0 I ] [ G21 G22 ] * * To keep optimal storage complexity, only G is stored, and * any blocks which are entirely zero have VNULL pointers. * * Basic Inputs: * * BXLN *M nodal mass matrix in doubly linked format * Bmat *R tails of the prolongation matrices (inside Algs) * int minLev coarsest level in the hierarchy * * Basic Outputs (inside the HBmat chain): * * Bmat *G21, *G22, *G12 logical blocks of G = S - I. * * The mass matrix can be safely passed as VNULL in the HB * case, since it is only touched in the WMHB case. *
| thee | Pointer to the HBmat object | |
| Ppro | tails of the prolongation matrices (inside Algs) 3 --> Standard HB 5 --> Wavelet Modified HB | |
| Mlink | nodal mass matrix in doubly linked format | |
| meth | method choice (0=Standard HB,1=Wavelet Modified HB) |
Assembles the hierarchical matrix structures for the HB Vcycle.
* Notes: This routine takes a null pointer to two HBmat pointers and * returns a linked (hierarchical) chain of fully assembled * HBmat's. * * Basic Inputs: * * Bmat *A the finest level stiffness matrix * Bmat *P0, *P1, ... the prologation matrices for each level * * Basic Outputs (inside the HBmat chain): * * Bmat *A21, *A22, *A12 stabilized Mat blocks on each level * Bmat *A11 stabilized A11 block on coarse level * Bvec *d1, *d2 defect section pointers * Bvec *r1, *r2 residual section pointers * * Example: Suppose we have a two-level system, resulting from a * mesh refinement. Let P be the prologation (restriction) * matrix which prolongates (restricts) a trial solution * from level 0 to 1 (1 to 0). The stiffness matrix, A, * can be naturally decomposed into four blocks, if the nodes * added during refinement (fine nodes) are logically * "appended" to the end of the solution vector: * * A = [ A11 A12 ] ; P = [ I ] ; d = [ d1 ] ; r = [ r1 ] * [ A21 A22 ] [ R ] [ d2 ] [ r2 ] * * Hierarchical Basis Multigrid (HB), doesn't use the standard * nodal basis, using instead the "hierarchical basis". The * HB-basis stiffness matrix is related to the nodal basis * stiffness matrix through a "change-of-basis" transform: * * A_hb = S'*A*S ; d = S*d_hb ; r_hb = S'*r ; S = [ I 0 ] * [ R I ] * Written out in blocks, A_hb has the form: * * A_hb = [ A11 + A12*R + R'*A21 + R'*A22*R ; A12 + R'*A22 ] * [ A21 + A22*R ; A22 ] * * The resulting HBmat and HBvec chains will have two levels, * 0 and 1, with a pointer to the chains returned as output. * Level 0 contains the only non-null pointer to A11. *
| Ahb | nodal stiffness matrix in doubly linked format | |
| Ghb | change of basis matrices for each level | |
| A | system matrix | |
| M | mass matrix | |
| Ppro | tails of the prolongation matrices (inside Algs) 3 --> Standard HB 5 --> Wavelet Modified HB | |
| meth | method choice (0=Standard HB,1=Wavelet Modified HB) |
Destruct the hierarchical structures.
| Ahb | nodal stiffness matrix in doubly linked format | |
| Ghb | change of basis matrices for each level |
| void HBmat_killStructure | ( | HBmat * | thee | ) |
Kills a chain of HBmat pointers.
| thee | Pointer to the HBmat object |
| void HBmat_printSp | ( | HBmat * | thee, | |
| char * | fname, | |||
| int | pflag | |||
| ) |
Print an HBmat in MATLAB sparse form.
| thee | Pointer to the HBmat object | |
| fname | character string name for the HBmatrix | |
| pflag | index for write/append |
1.5.6