Unit
Chair of Computational Mathematics and Simulation Science
LaboratoryRelated publications (214)
Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations
This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
EPFL2021Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks
Jan Sickmann Hesthaven, Deep Ray, Lukas Schwander
While a nonlinear viscosity is used widely to control oscillations when solving conservation laws using high-order elements based methods, such techniques are less straightforward to apply in global spectral methods since a local estimate of the solution r ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2021On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method
The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...
Springer-Verlag2021Structure-Preserving Reduced Basis Methods For Poisson Systems
Jan Sickmann Hesthaven, Cecilia Pagliantini
We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...
AMER MATHEMATICAL SOC2021Substructured Two-grid and Multi-grid Domain Decomposition Methods
Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...
2021Physics Informed Neural Networks for Surrogate Modelling and Inverse Problems in Geotechnics
Finite elements methods (FEMs) have benefited from decades of development to solve partial differential equations (PDEs) and to simulate physical systems. In the recent years, machine learning (ML) and artificial neural networks (ANN) have shown great pote ...
2021An arbitrary-order Cell Method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations
We introduce a new numerical method for the time-dependent Maxwell equations on unstructured meshes in two space dimensions. This relies on the introduction of a new mesh, which is the barycentric-dual cellular complex of the starting simplicial mesh, and ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2021Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide a fully discret ...
EPFL2021An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation
The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schrödinger equations. However, when applied to certain nonlinear time-dependent Schrödinger equations, this algorithm loses time reversibility and seco ...
2021On the asymptotic optimality of spectral coarse spaces
This paper is concerned with the asymptotic optimality of spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very ef ...
Springer-Verlag2021