Some Experiments and Issues to Exploit Multicore Parallelism in a Distributed-Memory Parallel Sparse Direct Solver

MUMPS is a parallel sparse direct solver, using message passing (MPI) for parallelism. In this report we experiment how thread parallelism can help taking advantage of recent multicore architectures. The work done consists in testing multithreaded BLAS libraries and inserting OpenMP directives in the routines revealed to be costly by profiling, with the objective to avoid any deep restructuring or rewriting of the code. We report on various aspects of this work, present some of the benefits and difficulties, and show that 4 threads per MPI process is generally a good compromise. We then discuss various issues that appear to be critical in a mixed MPI-OpenMP environment

Time integration and steady-state continuation for 2d lubrication equations

Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. In both algorithms a Cayley transform is employed to overcome numerical problems resulting from scale separation in space and time. An adaptive time-step allows to study the dynamics close to hetero- or homoclinic connections. The developed framework is employed on the one hand to analyse different phases of the dewetting of a liquid film on a horizontal homogeneous substrate. On the other hand, we consider the depinning of drops pinned by a wettability defect. Time-stepping and path-following are used in both cases to analyse steady-state solutions and their bifurcations as well as dynamic processes on short and long time-scales. Both examples are treated for two- and three-dimensional physical settings and prove that the developed algorithms are reliable and efficient for 1d and 2d lubrication equations, respectively.Comment: 33 pages, 16 figure

Design of a parallel hybrid direct/iterative solver for CFD problems

We discuss the parallel implementation of a hybrid direct/iterative solver for a special class of saddle point matrices arising from the discretization of the steady Navier-Stokes equations on an Arakawa C-grid, the F-matrices. The two-level method described here has the following properties: (i) it is very robust, even hat comparatively high Reynolds Numbers; (ii) a single parameter controls fill and convergence, making the method straightforward to use; (iii) the convergence rate is independent of the number of unknowns; (iv) it can be implemented on distributed memory machines in a natural way; (v) the matrix on the second level has the same structure and numerical properties as the original problem, so the method can be applied recursively. The implementation focusses on generality, modularity, code reuse and recursiveness. The solver is implemented using building blocks of the Trilinos libraries. We show its performance on a parallel computer for the Navier-Stokes equations

The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques

The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, its implementation remains challenging as it relies on geometrical projections and unconventional quadrature rules. The INTERNODES (INTERpolation for NOn-conforming DEcompositionS) method, instead, could overcome the implementation difficulties thanks to flexible interpolation techniques. Moreover, it was shown to be at least as accurate as the mortar method making it a very promising alternative for solving problems in contact mechanics. Unfortunately, in such situations the method requires solving a sequence of ill-conditioned linear systems. In this paper, preconditioning techniques are designed and implemented for the efficient solution of those linear systems