| Author | V. Korneev, J. E. Flaherty, T. Oden and J. Fish |
|---|---|
| Title | Additive Schwarz Algorithms for Solving hp-Version Finite Element Systems on Triangular Meshes |
| Year | 1999 |
| Journal | Applied Numerical Mathematics |
| Volume | 43 |
| Pages | 399-421 |
| Issue | 4 |
| Publisher | Elsevier Science Publishers B. V. |
| Abstract | Highly parallelizable domain decomposition Dirichlet-Dirichlet solvers for hp-version finite element methods on angular quasiuniform triangular meshes are studied under different assumptions on a reference element. The edge coordinate functions of a reference element are allowed to be either nodal, with special choices of nodes, or hierarchical polynomials of several types. In relation to the definition of these coordinate functions within the elements, we also distinguish two cases: arbitrary and so-called discrete quasi-harmonic coordinate functions. The latter are obtained by means of explicitly given and nonexpensive prolongation operators. In all these situations, we are able to suggest preconditioners which are spectrally equivalent to the global stiffness matrix, which require only the element-by-element and edge-by-edge operations and reduce the computational cost. In this way, elimination is avoided when dealing with an interface problem. In our domain decomposition algorithms, we essentially use prolongation operators from the interface boundary inside the subdomains of the decomposition according to the approach initially used for the hp-version with quadrilateral elements. |
| PDF File |  Download |