Hybrid parallelization of an adaptive finite element code

summary:We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the large problem and the smaller sub-problems, sufficiently fast we make use of a hierarchical mesh structure. The partitioning is done on a coarser mesh level, resulting in a very fast method that shows good computational balancing results. Numerical experiments show that both parallelization methods achieve good scalability in computing solution of nonlinear, time dependent, higher order PDEs on large domains. The parallelization is realized in the adaptive finite element software AMDiS

Design and Analysis of a Task-based Parallelization over a Runtime System of an Explicit Finite-Volume CFD Code with Adaptive Time Stepping

FLUSEPA (Registered trademark in France No. 134009261) is an advanced simulation tool which performs a large panel of aerodynamic studies. It is the unstructured finite-volume solver developed by Airbus Safran Launchers company to calculate compressible, multidimensional, unsteady, viscous and reactive flows around bodies in relative motion. The time integration in FLUSEPA is done using an explicit temporal adaptive method. The current production version of the code is based on MPI and OpenMP. This implementation leads to important synchronizations that must be reduced. To tackle this problem, we present the study of a task-based parallelization of the aerodynamic solver of FLUSEPA using the runtime system StarPU and combining up to three levels of parallelism. We validate our solution by the simulation (using a finite-volume mesh with 80 million cells) of a take-off blast wave propagation for Ariane 5 launcher.Comment: Accepted manuscript of a paper in Journal of Computational Scienc

Accurate and efficient algorithms for boundary element methods in electromagnetic scattering: a tribute to the work of F. Olyslager

Boundary element methods (BEMs) are an increasingly popular approach to model electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullulated from the research into BEMs, enhancing its efficiency and applicability. In designing a viable implementation of the BEM, both theoretical and practical aspects need to be taken into account. Theoretical aspects include the choice of an integral equation for the sought after current densities on the geometry's boundaries and the choice of a discretization strategy (i.e. a finite element space) for this equation. Practical aspects include efficient algorithms to execute the multiplication of the system matrix by a test vector (such as a fast multipole method) and the parallelization of this multiplication algorithm that allows the distribution of the computation and communication requirements between multiple computational nodes. In honor of our former colleague and mentor, F. Olyslager, an overview of the BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from F. Olyslager's scientific endeavors are included in the survey

A scalable H-matrix approach for the solution of boundary integral equations on multi-GPU clusters

In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our existing single-GPU hierarchical matrix library hmglib such that it is able to scale on many GPUs and such that it can be coupled to arbitrary application codes. Using a model GPU implementation of a boundary element method (BEM) solver, we are able to achieve more than 67 percent relative parallel speed-up going from 128 to 1024 GPUs for a model geometry test case with 1.5 million unknowns and a real-world geometry test case with almost 1.2 million unknowns. On 1024 GPUs of the cluster Titan, it takes less than 6 minutes to solve the 1.5 million unknowns problem, with 5.7 minutes for the setup phase and 20 seconds for the iterative solver. To the best of the authors' knowledge, we here discuss the first fully GPU-based distributed-memory parallel hierarchical matrix Open Source library using the traditional H-matrix format and adaptive cross approximation with an application to BEM problems