Related papers: Error estimate for semi-implicit method of sphere-…
The high-index saddle dynamics (HiSD) method is a powerful approach for computing saddle points and solution landscape. However, its practical applicability is constrained by the need for the explicit energy function expression. To overcome…
The aim of this work is to apply a semi-implicit (SI) strategy within a Rosenbrock-type and IMEX linear multistep (LM) framework to a sequence of 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives.…
We describe a mesh-free three-dimensional numerical scheme for solving the incompressible semi-geostrophic equations based on semi-discrete optimal transport techniques. These results generalise previous two-dimensional implementations. The…
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…
Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the…
Recent advances show that semi-supervised implicit representation learning can be achieved through physical constraints like Eikonal equations. However, this scheme has not yet been successfully used for LiDAR point cloud data, due to its…
We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…
We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for which a "good" macroscopic description in the form of…
We develop a semi-discrete optimal transport scheme for the compressible semi-geostrophic equations, a system that plays an important role in modelling large-scale atmospheric dynamics and frontogenesis. Unlike the incompressible case, the…
In this paper, we present a numerical analysis of the hydrostatic Stokes equations, which are linearization of the primitive equations describing the geophysical flows of the ocean and the atmosphere. The hydrostatic Stokes equations can be…
Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…
The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-volume numerical methods for 1D systems of balance laws. The strategy introduced by two of the authors in a previous paper for explicit schemes…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule…
We propose new semi-implicit numerical methods for the integration of the stochastic Landau-Lifshitz equation with built-in angular momentum conservation. The performance of the proposed integrators is tested on the 1D Heisenberg chain. For…