Related papers: High Order Boundary Extrapolation Technique for Fi…
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted…
Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
In this paper, we design a new kind of high order inverse Lax-Wendroff (ILW) boundary treatment for solving hyperbolic conservation laws with finite difference method on a Cartesian mesh. This new ILW method decomposes the construction of…
High order numerical methods for networks of hyperbolic conservation laws have recently gained increasing popularity. Here, the crucial part is to treat the boundaries of the single (one-dimensional) computational domains in such a way that…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
Extrapolation to out-of-distribution conditions is a fundamental challenge for physics-constrained deep generative models. Existing methods apply physical constraints as a single static regularization term uniformly across the generation…
An arbitrary order finite difference method for curved boundary domains with Cartesian grid is proposed. The technique handles in a universal manner Dirichlet, Neumann or Robin condition. We introduce the Reconstruction Off-site Data (ROD)…
This paper serves to treat boundary conditions numerically with high order accuracy in order to match the two-stage fourth-order finite volume schemes for hyperbolic problems developed in [{\em J. Li and Z. Du, A two-stage fourth order…
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure…
A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact…
We address the issue of point value reconstructions from cell averages in the context of third order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques known in the…
The problem of solution transfer between meshes arises frequently in computational physics, e.g. in Lagrangian methods where remeshing occurs. The interpolation process must be conservative, i.e. it must conserve physical properties, such…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497--A519 (2012)] to elliptic problems with mixed boundary conditions and elliptic…
Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…