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We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…

Numerical Analysis · Mathematics 2021-02-23 Stefan Dohr , Michal Merta , Günther Of , Olaf Steinbach , Jan Zapletal

In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2022-01-20 Aleksei Tyrylgin , Maria Vasilyeva , Anatoly Alikhanov , Dongwoo Sheen

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…

Numerical Analysis · Mathematics 2009-03-06 Igor Podlubny , Aleksei V. Chechkin , Tomas Skovranek , YangQuan Chen , Blas M. Vinagre Jara

We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…

Numerical Analysis · Mathematics 2018-07-27 Yingjun Jiang , Xuejun Xu

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…

Computational Engineering, Finance, and Science · Computer Science 2022-01-12 Andreas Hessenthaler , Robert D. Falgout , Jacob B. Schroder , Adelaide de Vecchi , David Nordsletten , Oliver Röhrle

In this work, we obtain the numerical temperature field to a thermally developing fluid flow inside parallel plates problem with a quantum computing method. The physical problem deals with the heat transfer of a steady state,…

This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal…

Analysis of PDEs · Mathematics 2020-05-05 Michael Ruzhansky , Niyaz Tokmagambetov , Berikbol T. Torebek

We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…

Plasma Physics · Physics 2008-12-01 Zoran Ristivojevic , Zoran Lj. Petrovic

An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence…

Numerical Analysis · Mathematics 2017-04-27 Jian Huang , Long Chen , Hongxing Rui

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

Numerical Analysis · Mathematics 2016-02-23 Josef Rebenda , Zdeněk Šmarda

Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a Partial Differential Equation (PDE), providing possibilities for accelerating the computation of its solution. While parallelisation in time has…

Numerical Analysis · Mathematics 2021-04-20 Federico Danieli , Scott MacLachlan

We study efficient simulation of steady state for rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following…

Numerical Analysis · Mathematics 2022-06-28 Zhicheng Hu , Guanghan Li

We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the…

Numerical Analysis · Mathematics 2024-02-27 Nicolas L. Guidotti , Juan Acebrón , José Monteiro

We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative…

Numerical Analysis · Mathematics 2020-09-21 Benjamin Rüth , Benjamin Uekermann , Miriam Mehl , Philipp Birken , Azahar Monge , Hans-Joachim Bungartz

In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…

General Mathematics · Mathematics 2023-05-30 Aymen Laadhari , Ahmad Deeb

In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a…

Numerical Analysis · Mathematics 2020-09-03 Allan P. Engsig-Karup , Wojciech Laskowski

In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the…

Numerical Analysis · Mathematics 2016-01-20 Arvind Baskaran , Zhen Guan , John Lowengrub

A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…

Geophysics · Physics 2009-11-10 Masanori Kameyama , Akira Kageyama , Tetsuya Sato

As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic…

Computational Physics · Physics 2016-11-30 Yunfeng Xiong , Zhenzhu Chen , Sihong Shao