Name
Abstract | ||
|---|---|---|
WeintroduceanewpreconditionerforellipticPDE'sonunstructuredmeshes. Using awavelet-inspiredbasiswecompresstheinverseofthematrix,allowinganeectiv e sparseapprox- imate inverse by solving the sparsity vs.accuracy conict. The key issue inthis compression isto use second-generation wavelets which can be adapted to the unstructured mesh, the true bound- ary conditions, and even the PDE coecien ts. We also show how this gives a new perspective on multiresolutionalgorithmssuchasmultigrid,interpreting the newpreconditioner asavariation on node-nestedmultigrid. Inparticular,wehopethenewpreconditionerwillcombinethebestofboth worlds: fast convergence when multilevel methods can succeed, but with robust performance for moredicult problems. Therestofthepaperdiscussesthecoreissuesforthepreconditioner: orderingandconstruction ofafactoredapproximateinverseinthemultiresolutionbasis,robustinterpolationonunstructured meshes, automatic mesh coarsening, and purely algebraic alternatives. Some exploratory numeri- cal experiments suggest the superiority of the new basis over the standard basis for several tough problems,includingdiscontinuousanisotropiccoecien ts,strongconvection,andindenite reaction problemsonunstructuredmeshes,withscalabilitylikehierarchicalbasismethodsachieved. |
Year | Venue | DocType |
|---|---|---|
2001 | SIAM Journal on Scientific Computing | Journal |
Volume | Issue | Citations |
23 | 2 | 0 |
PageRank | References | Authors |
0.34 | 7 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| ROBERT BRIDSON | 1 | 546 | 27.92 |
| Wei-Pai Tang | 2 | 96 | 34.36 |