相关论文: Arbitrary high-order methods for one-sided direct …
The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…
We propose a novel efficient algorithm to solve Poisson equation in irregular two dimensional domains for electrostatics. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
We study a convex optimization framework for bounding extreme events in nonlinear dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs). This framework bounds from above the largest value of an observable…
The incompressible Euler equations are an important model system in computational fluid dynamics. Fast high-order methods for the solution of this time-dependent system of partial differential equations are of particular interest: due to…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
This paper studies explicitly solvable multidimensional optimal stopping problems of sum- and product-type in discrete and continuous time using the monotone case approach. It gives a review on monotone case stopping using the Doob…
This paper addresses the numerical solution of the Westervelt equation, which arises as one of the model equations in nonlinear acoustics. The problem is rewritten in a canonical form that allows the systematic discretization by Galerkin…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequality formulation. The method admits an equivalent strictly…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
In this paper we study strong solutions of some non-local difference-differential equations linked to a class of birth-death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
A nonlocal contact problem for two-dimensional linear elliptic equations is stated and investigated. The method of separation of variables is used to find the solution of a stated problem in case of Poisson's equation. Then the more general…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization.…
We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…
We show that applying any deterministic B-series method of order $p_d$ with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order $\lfloor p_d/2\rfloor$.As an…
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with…