
Efficient implementation of partitioned stiff exponential RungeKutta methods
Multiphysics systems are driven by multiple processes acting simultaneou...
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EPIRKW and EPIRKK time discretization methods
Exponential integrators are special time discretization methods where th...
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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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Exponential Polynomial Time Integrators
In this paper we extend the polynomial time integration framework to inc...
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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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Efficient exponential Runge–Kutta methods of high order: construction and implementation
Exponential Runge–Kutta methods have shown to be competitive for the tim...
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Variance of finite difference methods for reaction networks with nonLipschitz rate functions
Parametric sensitivity analysis is a critical component in the study of ...
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Partitioned Exponential Methods for Coupled Multiphysics Systems
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semidiscretization in space, the class of problems under consideration are modeled by a system of ordinary differential equations where the righthand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitionedexponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. The traditional approach to constructing exponential methods, based on the variationofconstants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitionedexponential families is based on a generalstructure additive formulation of the schemes. Two method formulations are considered, one based on a linearnonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (nonstiff) order conditions theory for partitioned exponential schemes based on particular families of Ttrees and Bseries theory. Several practical methods of third order are constructed that extend the Rosenbrocktype and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reactiondiffusion systems are also discussed. Numerical experiments reveal that the new partitionedexponential methods can perform better than traditional unpartitioned exponential methods on some problems.
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