The FastMat2 Matrix Library. Description and Parallel Implementation

STORTI M.; CASTRO, HUGO GUILLERMO; PAZ RODRIGO; DALCÍN LISANDRO

Tandil

Congreso; XVIII Congreso sobre Métodos Numéricos y sus Aplicaciones; 2009

Asociación Argentina de Mecánica Computacional AMCA

Finite element codes usually have two levels of programming. At the outer level a series of nested loops for time stepping, or Newton iteration, leads to a series of linear problems that require residual and matrix assemblies which are then solved with iterative solvers like CG (for Conjugate Gra- dient) or GMRES (Generalized Minimal Residual Method). At the inner level, these assemblies are performed with a loop over all the elements in the mesh. The residual and matrix are computed for each element assembled in the global vector/matrix. The FastMat2 class is the main matrix library used in the PETSc-FEM code (http://www.cimec.org.ar/petscfem) for computations at the element level. It is full multi-index and performs the standard matrix functions like addition, tensor contractions (in the matrix sense and element-by-element), eigenvalue decomposition, inversion. A key point in its design is that many logical operations (row or column selections for instance) are the same for each element. So this kind of operations are cached in a Direct Acyclic Graph structure (DAG). Its implementation, in particular in a shared memory with OpenMP (for Open Multi-Processing) environment is discussed.