Related papers: A Parallel Time-Integrator for Solving the Lineari…
In this work, we present a novel class of parallelizable high-order time integration schemes for the approximate solution of additive ODEs. The methods achieve high order through a combination of a suitable quadrature formula involving…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion,…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…
Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…
ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are…
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from producing posterior distributions over ODE solutions and…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hydrodynamics. The efficiency stems from exploiting a…
Numerical solutions to the Eikonal equation are computed using variants of the fast marching method, the fast sweeping method, and the fast iterative method. In this paper, we provide a unified view of these algorithms that highlights their…
The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address…
Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature. Existing solver-based acceleration methods often face significant image quality…
The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and…
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to a…
We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the…
As we stride toward the exascale era, due to increasing complexity of supercomputers, hard and soft errors are causing more and more problems in high-performance scientific and engineering computation. In order to improve reliability…
A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method which ensures the convergent numerical solution. The main features include: (i) the memory usage is…
Recent advances in data collection technologies have led to the emergence of massive spatial datasets, with measurements obtained at millions of spatial locations. Geostatistical models typically employ Gaussian processes (GPs) to capture…
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…