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Stable and efficient quantum mechanical calculations with PUMA on triclinic lattices. (English) Zbl 1434.82097
Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations IX. Selected papers of the ninth international workshop, Bonn, Germany, September 18–20, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 129, 185-195 (2019).
Summary: In this paper we are concerned with the efficient approximation of the Schrödinger eigenproblem using an orbital-enriched flat-top partition of unity method on general triclinic cells. To this end, we generalize the approach presented in [the first author et al., Comput. Methods Appl. Mech. Eng. 342, 224–239 (2018; Zbl 1440.65163)] via a simple yet effective transformation approach and discuss its realization in the PUMA software framework. The presented results clearly show that the proposed scheme attains all convergence and stability properties presented in [loc. cit.].
For the entire collection see [Zbl 1422.65012].
MSC:
82M10 Finite element, Galerkin and related methods applied to problems in statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J10 Schrödinger operator, Schrödinger equation
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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