相关论文: The "Sphered Cube": A New Method for the Solution …

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding…

The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…

Cauchy problems with SPDEs on the whole space are localized to Cauchy problems on a ball of radius $R$. This localization reduces various kinds of spatial approximation schemes to finite dimensional problems. The error is shown to be…

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…

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…

We develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that…

In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…

This paper presents a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual…

The present work extends the direct-forcing immersed boundary method introduced by Garc\'ia-Villalba et al. (2023), broadening its application from spherical to arbitrarily-shaped particles, while maintaining its capacity to address both…

The classification of solutions to semilinear partial differential equations, as well as the classification of critical points of the corresponding functionals, have wide applications in the study of partial differential equations and…

We introduce a technique to solve numerically the relativistic Euler's equations in scenarios with spherical symmetry using the standard Smoothed Particles Hydrodynamics method in cartesian coordinates. This implementation allow us to…

This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…

We seek discrete approximations to solutions $u:\Omega \to R$ of semilinear elliptic partial differential equations of the form $\Delta u + f_s(u) = 0$, where $f_s$ is a one-parameter family of nonlinear functions and $\Omega$ is a domain…

The main objective of this article is to study the effect of spherical geometry on dynamic transitions and pattern formation for the Rayleigh-Benard convection. The study is mainly motivated by the importance of spherical geometry and…

The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…

In the recent developments of regularization theory for inverse and ill-posed problems, a variational quasi-reversibility (QR) method has been designed to solve a class of time-reversed quasi-linear parabolic problems. Known as a PDE-based…

A common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor-product multi-dimensional logical domain, which is mapped to a physical domain through a given coordinate…

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with…

Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…