Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
We consider the numerical approximation of a general second-order semilinear parabolic
stochastic partial differential equation driven by multiplicative and additive space–time …
stochastic partial differential equation driven by multiplicative and additive space–time …
A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms
When laboratory-measured chemical reaction rates are used in simulations at the field-
scale, the models typically overpredict the apparent reaction rates. The discrepancy is …
scale, the models typically overpredict the apparent reaction rates. The discrepancy is …
Comparison of software for computing the action of the matrix exponential
The implementation of exponential integrators requires the action of the matrix exponential
and related functions of a possibly large matrix. There are various methods in the literature …
and related functions of a possibly large matrix. There are various methods in the literature …
What can we learn from high-resolution numerical simulations of single-and multi-phase fluid flow in fractured outcrop analogues?
S Geiger, S Matthäi - Geological Society, London, Special …, 2014 - lyellcollection.org
Naturally fractured reservoirs (NFR), such as the large carbonate reservoirs in the Middle
East, contain a major part of the world's remaining conventional oil reserves, but recovering …
East, contain a major part of the world's remaining conventional oil reserves, but recovering …
Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg–Landau equation
We investigate localized wave solutions in a network of Hindmarsh–Rose neural model
taking into account the long-range diffusive couplings. We show by a specific analytical …
taking into account the long-range diffusive couplings. We show by a specific analytical …
Exponential methods for solving hyperbolic problems with application to collisionless kinetic equations
N Crouseilles, L Einkemmer, J Massot - Journal of Computational Physics, 2020 - Elsevier
The efficient numerical solution of many kinetic models in plasma physics is impeded by the
stiffness of these systems. Exponential integrators are attractive in this context as they …
stiffness of these systems. Exponential integrators are attractive in this context as they …
Weak convergence for a stochastic exponential integrator and finite element discretization of stochastic partial differential equation with multiplicative & additive noise
A Tambue, JMT Ngnotchouye - Applied Numerical Mathematics, 2016 - Elsevier
We consider a finite element approximation of a general semi-linear stochastic partial
differential equation (SPDE) driven by space-time multiplicative and additive noise. We …
differential equation (SPDE) driven by space-time multiplicative and additive noise. We …
Equivalence between the DPG method and the exponential integrators for linear parabolic problems
Abstract The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators
are two well established numerical methods for solving Partial Differential Equations (PDEs) …
are two well established numerical methods for solving Partial Differential Equations (PDEs) …
Exploiting the Kronecker product structure of φ−functions in exponential integrators
J Muñoz‐Matute, D Pardo… - International Journal for …, 2022 - Wiley Online Library
Exponential time integrators are well‐established discretization methods for time semilinear
systems of ordinary differential equations. These methods use φ− functions, which are matrix …
systems of ordinary differential equations. These methods use φ− functions, which are matrix …
Efficient simulation of geothermal processes in heterogeneous porous media based on the exponential Rosenbrock–Euler and Rosenbrock-type methods
Simulation of geothermal systems is challenging due to coupled physical processes in
highly heterogeneous media. Combining the exponential Rosenbrock–Euler method and …
highly heterogeneous media. Combining the exponential Rosenbrock–Euler method and …