Related papers: A robust solver for large-scale heat transfer topo…
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…
Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…
We study a conservative 5-point cell-centered finite volume discretization of the high-contrast diffusion equation. We aim to construct preconditioners that are robust with respect to the magnitude of the coefficient contrast and the mesh…
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…
This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological…
Predicting effective thermal conductivity by solving a Partial Differential Equation (PDE) defined on a high-resolution Representative Volume Element (RVE) is a computationally intensive task. In this paper, we tackle the task by proposing…
The numerical modeling of fracture contact thermo-poromechanics is crucial for advancing subsurface engineering applications, including CO2 sequestration, production of geo-energy resources, energy storage and wastewater disposal…
The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…
It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint…
We investigate the performance of a hybrid plasma solver on the test problem of an ion beam. The parallel solver is based on cell centered finite differences in space, and a predictor-corrector leapfrog scheme in time. The implementation is…
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…