30,359 research outputs found
Extrapolation-based implicit-explicit general linear methods
For many systems of differential equations modeling problems in science and
engineering, there are natural splittings of the right hand side into two
parts, one non-stiff or mildly stiff, and the other one stiff. For such systems
implicit-explicit (IMEX) integration combines an explicit scheme for the
non-stiff part with an implicit scheme for the stiff part.
In a recent series of papers two of the authors (Sandu and Zhang) have
developed IMEX GLMs, a family of implicit-explicit schemes based on general
linear methods. It has been shown that, due to their high stage order, IMEX
GLMs require no additional coupling order conditions, and are not marred by
order reduction.
This work develops a new extrapolation-based approach to construct practical
IMEX GLM pairs of high order. We look for methods with large absolute stability
region, assuming that the implicit part of the method is A- or L-stable. We
provide examples of IMEX GLMs with optimal stability properties. Their
application to a two dimensional test problem confirms the theoretical
findings
Extrapolated Implicit–Explicit Runge–Kutta Methods
We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by stage values in the previous step. This approach was first proposed by the authors in context of implicit–explicit general linear methods
Extrapolated Implicit–Explicit Runge–Kutta Methods
We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by stage values in the previous step. This approach was first proposed by the authors in context of implicit–explicit general linear methods
Extrapolation-Based Implicit-Explicit Peer Methods with Optimised Stability Regions
In this paper we investigate a new class of implicit-explicit (IMEX) two-step
methods of Peer type for systems of ordinary differential equations with both
non-stiff and stiff parts included in the source term. An extrapolation
approach based on already computed stage values is applied to construct IMEX
methods with favourable stability properties. Optimised IMEX-Peer methods of
order p = 2, 3, 4, are given as result of a search algorithm carefully designed
to balance the size of the stability regions and the extrapolation errors.
Numerical experiments and a comparison to other implicit-explicit methods are
included.Comment: 21 pages, 6 figure
Extrapolation-Based Super-Convergent Implicit-Explicit Peer Methods with A-stable Implicit Part
In this paper, we extend the implicit-explicit (IMEX) methods of Peer type
recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203--215, 2017]
to a broader class of two-step methods that allow the construction of
super-convergent IMEX-Peer methods with A-stable implicit part. IMEX schemes
combine the necessary stability of implicit and low computational costs of
explicit methods to efficiently solve systems of ordinary differential
equations with both stiff and non-stiff parts included in the source term. To
construct super-convergent IMEX-Peer methods with favourable stability
properties, we derive necessary and sufficient conditions on the coefficient
matrices and apply an extrapolation approach based on already computed stage
values. Optimised super-convergent IMEX-Peer methods of order s+1 for s=2,3,4
stages are given as result of a search algorithm carefully designed to balance
the size of the stability regions and the extrapolation errors. Numerical
experiments and a comparison to other IMEX-Peer methods are included.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1610.0051
TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness
This data set contains the data accompanying the article F. Denner and B. van Wachem, TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness, Journal of Computational Physics (2015), http://dx.doi.org/10.1016/j.jcp.2015.06.008.This data set contains the data accompanying the article F. Denner and B. van Wachem, TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness, Journal of Computational Physics (2015), http://dx.doi.org/10.1016/j.jcp.2015.06.008
- …