arXiv subjects

Sanjib Kumar Acharya

Publications and source records attributed to Sanjib Kumar Acharya.

5 recordsLinked to original sources

arXiv2025

Vectorized 3D mesh refinement and implementation of primal hybrid FEM in MATLAB

In this article, we introduce a Face-to-Tetrahedron connectivity in MATLAB together with a vectorized 3D uniform mesh refinement technique. We introduce a MATLAB vectorized assembly of 3D lowest-order primal hybrid finite element matrices for a second-order elliptic problem. We introduce a parallel solver and a vectorized Schur complement solver to solve the associated linear problem. The numerical results illustrate the software's runtime performance.

math.NA↗

arXiv2024

Vectorized implementation of primal hybrid FEM in MATLAB

We present efficient MATLAB implementations of the lowest-order primal hybrid finite element method (FEM) for linear second-order elliptic and parabolic problems with mixed boundary conditions in two spatial dimensions. We employ the Crank-Nicolson finite difference scheme for the complete discrete setup of the parabolic problem. All the codes presented are fully vectorized using matrix-wise array operations. Numerical experiments are conducted to show the performance of the software.

math.NA↗

arXiv2021

Additive Average Schwarz Method for Elliptic Mortar Finite Element Problems with Highly Heterogeneous Coefficients

In this paper, we extend the additive average Schwarz method to solve second order elliptic boundary value problems with heterogeneous coefficients inside the subdomains and across their interfaces by the mortar technique, where the mortar finite element discretization is on nonmatching meshes. In this two-level method, we enrich the coarse space in two different ways, i.e., by adding eigenfunctions of two variants of the generalized eigenvalue problems. We prove that the condition numbers of the systems of algebraic equations resulting from the extended additive average Schwarz method, corresponding to both coarse spaces, are of the order O(H/h) and independent of jumps in the coefficients, where H and h are the mesh parameters.

math.NA↗

arXiv2018

A priori error analysis of the $hp$-mortar FEM for parabolic problems

In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms. The superconvergence results for the solution of the semidiscrete problem are studied in an eqivalent negative norm, with an extra regularity assumption. Numerical experiments are conducted to validate the theoretical findings.

math.AP↗

arXiv2017

Convergence results with natural norms: Stabilized Lagrange multiplier method for elliptic interface problems

A stabilized Lagrange multiplier method for second order elliptic interface problems is presented in the framework of mortar method. The requirement of LBB (Ladyzhenskaya-Babuška-Brezzi) condition for mortar method is alleviated by introducing penalty terms in the formulation. Optimal convergence results are established in natural norm which is independent of mesh. Numerical experiments are conducted in support of the theoretical derivations.

math.NA↗