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We consider a three-level parallelisation scheme. The second and third levels define a classical two-level parallelisation scheme and some load balancing algorithm is used to distribute tasks among processes. It is well-known that for many…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…
In this study, we present a parallel topology algorithm with a suitable interpolation method for chimera simulations in CFD. The implementation is done in the unstructured Finite Volume (FV) framework and special attention is given to the…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes,…
We present a simple mathematical framework and API for parallel mesh and data distribution, load balancing, and overlap generation. It relies on viewing the mesh as a Hasse diagram, abstracting away information such as cell shape,…
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit…
The research of two-level overlapping Schwarz (TL-OS) method based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g. mainly for second order elliptic problem and too heavy…
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…
Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…
This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next decade. Often one endeavours…
We investigate non-overlapping Schwarz preconditioners for the algebraic systems stemming from high-order discretizations of the coupled monodomain and Barreto-Cressman models, with applications to brain electrophysiology. The spatial…
We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…
This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…