Related papers: Multigrid waveform relaxation for the time-fractio…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…