A Scalable and Modular Software Architecture for Finite Elements on Hierarchical Hybrid Grids

In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers. Combining an unstructured topology with structured grid refinement facilitates high geometric adaptability and matrix-free multigrid implementations with excellent performance. Different abstraction levels and fully distributed data structures additionally ensure high flexibility, extensibility, and scalability. The software concepts support sophisticated load balancing and flexibly combining finite element spaces. Example scenarios with coupled systems of PDEs show the applicability of the concepts to performing geophysical simulations.Comment: Preprint of an article submitted to International Journal of Parallel, Emergent and Distributed Systems (Taylor & Francis

Preparing sparse solvers for exascale computing.

Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'

The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis

A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers lowcost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale quadrature. To generate surrogate matrices, quadrature must only be performed on a fraction of the elements in the computational domain. In this way, quadrature determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. We present the modifications and extensions required for a reference implementation in the open-source IGA software library GeoPDEs. The exposition is fashioned to help facilitate similar modifications in other contemporary software libraries. Method name: Surrogate matrix method for isogeometric analysi