Parallel Iterative Solution of Finite Element Systems of Equations Employing Edge-Based Data Structures.
Marcos A. D. Martins, Álvaro L. G. A. Coutinho, José L. D. Alves · 1997
This work presents optimization techniques for the sparse matrix-vector multiplication needed in the conjugate gradient solution of finite element systems of equations on unstructured grids composed by triangles or tetrahedra. The optimization techniques are based on the transition from a conventional element-by-element to an edge-by-edge data structure. Implementation considers the vectorization and parallelization capabilities of current shared memory supercomputers. In the solution of large scale industrial configurations, we observed considerable improvements when using edge-based schemes. 1 Introduction The application of implicit finite element formulations to engineering problems (linear or nonlinear, steady or transient) requires the solution of a system of linear equations at each time step and/or iteration. In general, it is possible to write these systems as, Ax = b (1) where A is a N \\Theta N sparse matrix, x is the vector of nodal unknowns and b is the out-ofbala...