Related papers: Comparative study of finite element methods using …
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of…
We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance ---in terms of both numerical…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…
In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
his paper presents finite element methods for solving numerically the Risk-Adjusted Pricing Methodology (RAPM) Black-Scholes model for option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are…
We address our attention to the numerical time discretization of stochastic Poisson systems via Poisson integrators. The aim of the investigation regards the backward error analysis of such integrators to reveal their ability of being…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
In order to learn distributed port-Hamiltonian systems (dPHS) using Gaussian processes (GPs), the partitioned finite element method (PFEM) is combined with the Gp-dPHS method. By following a late lumping approach, the discretization of the…
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…
A method for automatic computation of parameter derivatives of numerically computed light scattering signals is demonstrated. The finite-element based method is validated in a numerical convergence study, and it is applied to investigate…
A commonly held view in the turbomachinery community is that finite element methods are not well-suited for very large-scale thermomechanical simulations. We seek to dispel this notion by presenting performance data for a collection of…
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach that combines differential and difference algebra to analyze s(trong)-consistency of finite difference approximations.…
We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random…
The spectral gradient method is known to be a powerful low-cost tool for solving large-scale optimization problems. In this paper, our goal is to exploit its advantages in the stochastic optimization framework, especially in the case of…