Adaptive technique for Chebyshev-Based solvers for three-dimensional elliptic equations

Elliptic Solvers for Adaptive Mesh Refinement Grids

We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms...

Reduced Systems for Three-Dimensional Elliptic Equations with Variable Coefficients

We consider large sparse nonsymmetric linear systems arising from finite difference discretization of three-dimensional (3D) convection-diffusion equations with variable coefficients. We show that performing one step of cyclic reduction yields a system of equations which is well conditioned and for which fast convergence can be obtained. A certain block ordering strategy is applied, and analyti...

Preconditioning techniques in Chebyshev collocation method for elliptic equations

When one approximates elliptic equations by the spectral collocation method on the Chebyshev-Gauss-Lobatto (CGL) grid, the resulting coefficient matrix is dense and illconditioned. It is known that a good preconditioner, in the sense that the preconditioned system becomes well conditioned, can be constructed with finite difference on the CGL grid. However, there is a lack of an efficient solver...

Fast direct solvers for elliptic partial differential equations

Adaptive frame methods for elliptic operator equations

Stephan Dahlke a, Massimo Fornasier b and Thorsten Raasch a a Philipps-Universität Marburg, FB 12 Mathematik und Informatik, Hans-Meerwein Straße, Lahnberge, 35032 Marburg, Germany E-mail: {dahlke;raasch}@mathematik.uni-marburg.de b Università “La Sapienza” in Roma, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Via Antonio Scarpa, 16/B, 00161 Roma, Italy E-mail: mfornasi...