Related papers: Neumann-Neumann Waveform Relaxation Algorithm in M…
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized nonlinear elliptic partial differential equations (PDEs) based on overlapping subdomains. Our approach reads as a constrained…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
We propose a method for solving the time independent Schr\"odinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al., New J. Phys.…
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…
This work presents a novel family of well-balanced numerical schemes for hyperbolic systems of balance laws based on the kinetic relaxation approach. The method begins by transforming the original non-linear system into a linearized kinetic…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for…
This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with…
Temporal alignment of multiple signals through time warping is crucial in many fields, such as classification within speech recognition or robot motion learning. Almost all related works are limited to data in Euclidean space. Although an…
Contact phenomena are essential in understanding the behavior of mechanical systems. Existing computational approaches for simulating mechanical contact often encounter numerical issues, such as inaccurate physical predictions, energy…
We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual…
To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not…
We present a fast algorithm for evaluating the (non-smooth) solution of the free-space two-dimensional (2D) scalar wave equation with many point sources, each with a high-frequency band-limited time signature. Such an algorithm is key to an…
This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. However, due to limitations in observation, e.g., limited…
We consider a time-dependent Schr\"odinger equation for the Friedmann-Robertson-Walker (FRW) model. We show that for this purpose it is possible to include an additional action invariant under reparametrization of time. The last one does…
We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned…
The aim of this article is to analyze numerical schemes using two-layer neural networks withinfinite width for the resolution of high-dimensional Schr{\"o}dinger eigenvalue problems with smoothinteraction potentials and Neumann boundary…