The Partition of Unity Finite Element Method for the Schrödinger Equation

• Published in: Journal of computational methods in applied mathematics Vol. 25; no. 1; pp. 39 - 60
• Main Authors: Boffi, Daniele, Certik, Ondrej, Gardini, Francesca, Manzini, Gianmarco
• Format: Journal Article
• Language: English
• Published: Minsk De Gruyter 01.01.2025; Walter de Gruyter GmbH
• Subjects: 34L16; 65L60; Boundary conditions; Chemical partition; Eigenvalues; Eigenvectors; Enriched Partition of Unity Finite Element Method; Exact solutions; Finite element analysis; Finite element method; Galerkin method; Mathematical analysis; Mathematics; Parallelepipeds; Plane waves; Quantum mechanics; Schrodinger equation; Schrödinger Eigenvalue Problem; Unit cell; Wave functions

A Schrödinger equation for the system’s wavefunctions in a parallelepiped unit cell subject to Bloch-periodic boundary conditions must be solved repeatedly in quantum mechanical computations to derive the materials’ properties. Recent studies have demonstrated how enriched finite element type Galerk...