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Item type:Publication, Access status: without files , Time parallel gravitational collapse simulation(2017-05-08); ; ; This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in time, a tailored load balancing scheme is proposed and compared to load balancing based on number of time steps alone. The performance of Parareal is studied for both the sub-critical and black hole case; our experiments show that Parareal generates substantial speedup and, in the super-critical regime, can reproduce Choptuik's black hole mass scaling law.Publicationtype: Journal Article46 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Parareal for diffusion problems with spaceand time-dependent coefficientsPublicationtype: Conference Paper94 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , 50 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Verification of cardiac mechanics software: Benchmark problems and solutions for testing active and passivematerial behaviour(2015-12-08); ; ; ; Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-Type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.Publicationtype: Journal Article57 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , 65 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A multi-level spectral deferred correction method(2015-09-30); ; ; ; The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. Three different strategies to reduce the computational cost of correction sweeps on the coarser levels are examined: reducing the degrees of freedom, reducing the order of the spatial discretization, and reducing the accuracy when solving linear systems arising in implicit temporal integration. Several numerical examples demonstrate the effect of multi-level coarsening on the convergence and cost of SDC integration. In particular, MLSDC can provide significant savings in compute time compared to SDC for a three-dimensional problem.Publicationtype: Journal Article45 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A stencil-based implementation of Parareal in the C++ domain specific embedded language STELLA(2015-09-15); ; In view of the rapid rise of the number of cores in modern supercomputers, time-parallel methods that introduce concurrency along the temporal axis are becoming increasingly popular. For the solution of time-dependent partial differential equations, these methods can add another direction for concurrency on top of spatial parallelization. The paper presents an implementation of the time-parallel Parareal method in a C++ domain specific language for stencil computations (STELLA). STELLA provides both an OpenMP and a CUDA backend for a shared memory parallelization, using the CPU or GPU inside a node for the spatial stencils. Here, we intertwine this node-wise spatial parallelism with the time-parallel Parareal. This is done by adding an MPI-based implementation of Parareal, which allows us to parallelize in time across nodes. The performance of Parareal with both backends is analyzed in terms of speedup, parallel efficiency and energy-to-solution for an advection-diffusion problem with a time-dependent diffusion coefficient.Publicationtype: Journal Article53 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Numerical simulation of skin transport using Parareal(2015-08-15); ; ; ; In silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms. This article investigates the applicability of the time-parallel Parareal algorithm to a brick and mortar setup, a precursory problem to skin permeation. The C++ library Lib4PrM implementing Parareal is combined with the UG4 simulation framework, which provides the spatial discretization and parallelization. The combination’s performance is studied with respect to convergence and speedup. It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal’s convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed.Publicationtype: Journal Article48 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Convergence of parareal for the Navier-Stokes equations depending on the Reynolds numberThe paper presents first a linear stability analysis for the time-parallel Parareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method as fine propagator, confirming that dominant imaginary eigenvalues negatively affect Parareal’s convergence. This suggests that when Parareal is applied to the nonlinear Navier-Stokes equations, problems for small viscosities could arise. Numerical results for a driven cavity benchmark are presented, confirming that Parareal’s convergence can indeed deteriorate as viscosity decreases and the flow becomes increasingly dominated by convection. The effect is found to strongly depend on the spatial resolution.Publicationtype: Conference Paper73 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Parallel-in-space-and-time simulation of the three-dimensional, unsteady Navier-Stokes equations for incompressible flowPublicationtype: Conference Paper54