
Partitioned Exponential Methods for Coupled Multiphysics Systems
Multiphysics problems involving two or more coupled physical phenomena a...
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Highorder partitioned spectral deferred correction solvers for multiphysics problems
We present an arbitrarily highorder, conditionally stable, partitioned ...
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Symplectic GARK methods for Hamiltonian systems
Generalized Additive RungeKutta schemes have shown to be a suitable too...
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Stabilized explicit multirate methods for stiff differential equations
Stabilized RungeKutta (aka Chebyshev) methods are especially efficient ...
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Dynamical analysis in a selfregulated system undergoing multiple excitations: first order differential equation approach
In this paper, we discuss a novel approach for studying longitudinal dat...
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Lanczoslike method for the timeordered exponential
The timeordered exponential is defined as the function that solves any ...
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Lanczoslike algorithm for the timeordered exponential: The ∗inverse problem
The timeordered exponential of a timedependent matrix A(t) is defined ...
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Efficient implementation of partitioned stiff exponential RungeKutta methods
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using exponential RungeKutta methods. We propose specific multiphysics implementations of exponential RungeKutta methods satisfying stiff order conditions that were developed in [Hochbruck et al., SISC, 1998] and [Luan and Osterman, JCAM, 2014]. We reformulate stiffly–accurate exponential Runge–Kutta methods in a way that naturally allows of the structure of multiphysics systems, and discuss their application to both component and additively partitioned systems. The resulting partitioned exponential methods only compute matrix functions of the Jacobians of individual components, rather than the Jacobian of the full, coupled system. We derive modified formulations of particular methods of order two, three and four, and apply them to solve a partitioned reactiondiffusion problem. The proposed methods retain full order for several partitionings of the discretized problem, including by components and by physical processes.
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