Related papers: Several new domain-type and boundary-type numerica…
This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
We present a new approach to parallelization of the first-order backward difference discretization (BDF1) of the time derivative in partial differential equations, such as the nonlinear heat and viscous Burgers equations. The time…
A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…
A fast method for solving boundary integral equations with the generalized Neumann kernel and the adjoint generalized Neumann kernel is presented. The method is based on discretizing the integral equations by the Nystr\"om method with the…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
This work addresses a novel version of the kernel-free boundary integral (KFBI) method for solving elliptic PDEs with implicitly defined irregular boundaries and interfaces. We focus on boundary value problems and interface problems, which…
Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…
Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations (PDEs) because they are flexible with respect to the geometry of the computational domain, they can…
We develop two unfitted finite element methods for the Stokes equations using $H^{\text{div}}$-conforming finite elements. Both methods achieve optimal convergence for velocity, ensure pointwise divergence-free velocity fields, and produce…
The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density…
Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…
This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…