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A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
Higher-order regularization problem formulations are popular frameworks used in machine learning, inverse problems and image/signal processing. In this paper, we consider the computational problem of finding the minimizer of the Sobolev…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…
We present a new algorithm for computing the quasi-stationary distribution of subcritical Galton--Watson branching processes. This algorithm is based on a particular discretization of a well-known functional equation that characterizes the…
This paper discusses energy-conserving time-discretizations for finite element particle-in-cell discretizations of the Vlasov--Maxwell system. A geometric spatially discrete system can be obtained using a standard particle-in-cell…
Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…
Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the…
The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of…
In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to…
We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations…
A discretization scheme for variable coefficient elliptic PDEs in the plane is presented. The scheme is based on high-order Gaussian quadratures and is designed for problems with smooth solutions, such as scattering problems involving soft…
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…
The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…