Computational Science Laboratory

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https://hdl.handle.net/10919/102074
The mission of the Computational Science Laboratory (CSL) is to develop innovative computational solutions for complex real-world problems, and to foster a productive research and education environment emphasizing collaboration and innovation.

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Browsing Computational Science Laboratory by Subject "0906 Electrical and Electronic Engineering"

Now showing 1 - 3 of 3
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    Alternating directions implicit integration in a general linear method framework
    Sarshar, Arash; Roberts, Steven; Sandu, Adrian (Elsevier, 2021-05-15)
    Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional equations. Classical ADI methods have order at most two, due to the splitting errors. Moreover, when the time discretization of stiff one-dimensional problems is based on Runge–Kutta schemes, additional order reduction may occur. This work proposes a new ADI approach based on the partitioned General Linear Methods framework. This approach allows the construction of high order ADI methods. Due to their high stage order, the proposed methods can alleviate the order reduction phenomenon seen with other schemes. Numerical experiments are shown to provide further insight into the accuracy, stability, and applicability of these new methods.
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    Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
    Hachtel, Christoph; Bartel, Andreas; Guenther, Michael; Sandu, Adrian (Elsevier, 2021-05-15)
    Systems of differential equations which consist of subsystems with widely different dynamical behaviour can be integrated by multirate time integration schemes to increase the efficiency. These schemes allow the usage of inherent step sizes according to the dynamical properties of the subsystem. In this paper, we extend the multirate implicit Euler method to semi-explicit differential–algebraic equations of index-1 where the algebraic constraints only occur in the slow changing subsystem. We discuss different coupling approaches and show that consistency and convergence order 1 can be reached. Numerical experiments validate the analytical results.
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    Subspace adaptivity in Rosenbrock-Krylov methods for the time integration of initial value problems
    Tranquilli, Paul; Glandon, Ross; Sandu, Adrian (Elsevier, 2021-03-15)
    The Rosenbrock–Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work proposes an extension of Rosenbrock–Krylov methods to address stability questions which arise for methods making use of inexact linear system solution strategies. Two approaches for improving the stability and efficiency of Rosenbrock–Krylov methods are proposed, one through direct control of linear system residuals and the second through a novel extension of the underlying Krylov space to include stage right hand side vectors. Rosenbrock–Krylov methods employing the new approaches show a substantial improvement in computational efficiency relative to prior implementations.