Design and data structure of fully adaptive, multigrid, finite-element software. (English) Zbl 0578.65112

Rivara, Maria-Cecilia

ACM Trans. Math. Softw. 10, 242-264 (1984).

The author presents software for dealing with the finite element method approach in order to solve numerically partial differential equations in the following context: a) conforming triangulations are used; b) adaptive mesh refinements are employed for the generation of grids; c) the multigrid method is applied to obtain the numerical solution. On the basis of a), b) and c), a general purpose algorithm is discussed; its flexibility can be useful when dealing with singular or nearly singular differential problems. The main point in the paper is the design of efficient data structure for that algorithm; to cope with this problem, the notion of molecular list structure is introduced. The paper also contains numerical examples and a heuristic confrontation with methods that employ direct solvers for a fixed discretization of the differential problem.

Reviewer: J.P.Milaszewicz

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65F10	Iterative numerical methods for linear systems

Keywords:

finite elements; adaptive refinements; multigrid method; data; structure; singular differential problems; numerical examples