相关论文: A hybrid interpolation ACA accelerated method for …
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method…
This paper presents a parallel-in-time multilevel iterative method for solving differential algebraic equation, arising from a discretization of linear time-dependent partial differential equation. The core of the method is the multilevel…
The present work addresses the Cauchy problem for an abstract nonlinear system of coupled hyperbolic equations associated with the Timoshenko model in a real Hilbert space. Our purpose is to develop and delve into a temporal discretization…
The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short time scale, the dynamics tend to a non-linear diffusion-type…
We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…
The Improved Partial Area-Analytical Calculation (IPA-AC) method represents a leading meshfree discretization strategy for peridynamic models, distinguished by its rigorous geometric treatment of boundary intersections via dual corrections…
A framework is presented to design multirate time stepping algorithms for two dissipative models with coupling across a physical interface. The coupling takes the form of boundary conditions imposed on the interface, relating the solution…
The Adaptive Cross Approximation (ACA) method is widely used to approximate admissible blocks of hierarchical matrices, or H-matrices, from discretized operators in the boundary integral method. These matrices are fully populated, making…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
This paper presents a large-scale parallel solver, specifically designed to tackle the challenges of solving high-dimensional and high-contrast linear systems in heat transfer topology optimization. The solver incorporates an interpolation…
We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by the…
In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into…
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.…
In this paper we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a $hp$-version discontinuous Galerkin finite element approximation in the time…
A parallel time integration method for nonlinear partial differential equations is proposed. It is based on a new implementation of the Paraexp method for linear partial differential equations (PDEs) employing a block Krylov subspace…
In this article we study the two dimensional singularly perturbed heat equation in a circular domain. The aim is to develop a numerical method with a uniform mesh, avoiding mesh refinement at the boundary thanks to the use of a relatively…
We leverage the proximal Galerkin algorithm (Keith and Surowiec, Foundations of Computational Mathematics, 2024, DOI: 10.1007/s10208-024-09681-8), a recently introduced mesh-independent algorithm, to obtain a high-order finite element…
We propose and analyze a space-time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space-time meshes. Existence and…
The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation,…
In this paper, we will present advanced discretization methods for solving retarded potential integral equations. We employ a $C^{\infty}$-partition of unity method in time and a conventional boundary element method for the spatial…