A generic finite element framework on parallel tree-based adaptive\n meshes

Abstract

In this work we formally derive and prove the correctness of the algorithms\nand data structures in a parallel, distributed-memory, generic finite element\nframework that supports h-adaptivity on computational domains represented as\nforest-of-trees. The framework is grounded on a rich representation of the\nadaptive mesh suitable for generic finite elements that is built on top of a\nlow-level, light-weight forest-of-trees data structure handled by a\nspecialized, highly parallel adaptive meshing engine, for which we have\nidentified the requirements it must fulfill to be coupled into our framework.\nAtop this two-layered mesh representation, we build the rest of data structures\nrequired for the numerical integration and assembly of the discrete system of\nlinear equations. We consider algorithms that are suitable for both\nsubassembled and fully-assembled distributed data layouts of linear system\nmatrices. The proposed framework has been implemented within the FEMPAR\nscientific software library, using p4est as a practical forest-of-octrees\ndemonstrator. A strong scaling study of this implementation when applied to\nPoisson and Maxwell problems reveals remarkable scalability up to 32.2K CPU\ncores and 482.2M degrees of freedom. Besides, a comparative performance study\nof FEMPAR and the state-of-the-art deal.ii finite element software shows at\nleast comparative performance, and at most factor 2-3 improvements in the\nh-adaptive approximation of a Poisson problem with first- and second-order\nLagrangian finite elements, respectively.\n