Matrix equation techniques for certain evolutionary partial differential equations

08/30/2019
by   Davide Palitta, et al.
0

We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines projection techniques with the full exploitation of the entry-wise structure of the involved coefficient matrices is proposed. The resulting scheme is able to efficiently solve problems with a tremendous number of degrees of freedom while maintaining a low storage demand as illustrated in several numerical examples.

READ FULL TEXT
research
03/12/2020

Numerical Approximation of Nonlinear SPDE's

The numerical analysis of stochastic parabolic partial differential equa...
research
04/05/2021

A decision-making machine learning approach in Hermite spectral approximations of partial differential equations

The accuracy and effectiveness of Hermite spectral methods for the numer...
research
05/07/2020

Delayed approximate matrix assembly in multigrid with dynamic precisions

The accurate assembly of the system matrix is an important step in any c...
research
02/05/2022

A practical algorithm to minimize the overall error in FEM computations

Using the standard finite element method (FEM) to solve general partial ...
research
10/28/2020

Explicit stabilized multirate method for stiff stochastic differential equations

Stabilized explicit methods are particularly efficient for large systems...
research
06/09/2021

Natural Factor Based Solvers

We consider parametric families of partial differential equations–PDEs w...
research
06/10/2021

Concurrent multi-parameter learning demonstrated on the Kuramoto-Sivashinsky equation

We develop an algorithm for the concurrent (on-the-fly) estimation of pa...

Please sign up or login with your details

Forgot password? Click here to reset