Related papers: Algebraic Stabilization of Explicit Numerical Inte…
The analytic deep prior (ADP) approach was recently introduced for the theoretical analysis of deep image prior (DIP) methods with special network architectures. In this paper, we prove that ADP is in fact equivalent to classical…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact…
Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS…
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…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
Many low-Mach or all-Mach number codes are based on space discretizations which in combination with the first order explicit Euler method as time integration would lead to an unstable scheme. In this paper, we investigate how the choice of…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature,…
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
Modern distributed systems often rely on so called weakly-consistent databases, which achieve scalability by sacrificing the consistency guarantee of distributed transaction processing. Such databases have been formalised in two different…
Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions…
We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic…