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Showing 1 to 8 of 8 for “"Exponential integrators"”.
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Exponential integrators: tensor structured problems and applications
… integrate such systems involves using exponential integrators. In general, these kinds of schemes do not require the solution of (non)linear systems but rather the action of the matrix exponential and of some specific exponential-like functions (known in the literature as φ-functions). …
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Exponential Integrators for the Incompressible Navier-Stokes Equations
… functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is …
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Numerical approximation of Stratonovich SDEs and SPDEs
… of time-differencing schemes which are based on exponential integrator techniques. We focus on the study of two numerical schemes, both appropriate for the simulation of Stratonovich- interpreted S(P)DEs. The first, is a basic strong order 1=2 scheme, called Stratonovich Exponential Integrators …
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Scalable High-Resolution Simulation of the Prey-Predator Model, with a Non-Local Consumption of Prey
… and Adaptive Krylov-Projection (AKP) exponential integrators on grids up to N = 8000 shows it maintains a constant iteration count of four Fast fourier tranforms (FFTs) per iteration, achieves relative errors below 10−8 and delivers result up to 40 times faster. Large-scale simulations …
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The analysis and implementation of exponential almost Runge-Kutta methods for semilinear problems
We look at two families of Exponential Integrators, the multi-step Exponential Time Differencing Methods and the multi-stage Exponential Runge-Kutta Methods. A broader framework of Exponential General Linear Methods builds on these two families. We extend the classical Almost Runge-Kutta Method …
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Polynomial-Based Methods for Time-Integration
… polynomials, and the second extends exponential integration to the spectral deferred correction framework. Both parts discuss time integration methods that can be derived without solving nonlinear order conditions. In part I, we introduce a time-integration framework for solving …
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Advanced Time Integration Methods with Applications to Simulation, Inverse Problems, and Uncertainty Quantification
… a posteriori error framework. We extend exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the …