Related papers: Parallel-in-Time Solution of Eddy Current Problems…
In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
In this article, we introduce a novel parallel-in-time solver for nonlinear ordinary differential equations (ODEs). We state the numerical solution of an ODE as a root-finding problem that we solve using Newton's method. The affine…
This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…
Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to…
Despite the growing interest in parallel-in-time methods as an approach to accelerate numerical simulations in atmospheric modelling, improving their stability and convergence remains a substantial challenge for their application to…
We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method…
Recently, ParaExp was proposed for the time integration of hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a…
Recent years have witnessed an unprecedented increase in experiments and hybrid simulations involving quantum computers. In particular, quantum annealers. Although quantum supremacy has not been established thus far, there exist a plethora…
Computing the electric eddy currents in non-linear materials, such as superconductors, is \E{not straightforward}. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a…
The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…
We consider an asynchronous system with transitions corresponding to the instructions of a computer system. For each instruction, a runtime is given. We propose a mathematical model, allowing us to construct an algorithm for finding the…
Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigenvalues. Since these methods can be parallelized in time (in…
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
The problem under consideration is that of time-harmonic eddy current problems in linear ferromagnetic materials surrounded by a dielectric medium with a smooth common interface. Assuming axisymmetric geometries and orthoradial axisymmetric…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large eddy…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
On modern parallel architectures, the cost of synchronization among processors can often dominate the cost of floating-point computation. Several modifications of the existing methods have been proposed in order to keep the communication…