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Sparse grids for the Schrödinger equation. (English) Zbl 1145.65096

The authors first present a sparse grid/hyperbolic cross discretization for many-particle problems, and then introduce an additional constraint which gives antisymmetric sparse grids which are suited to fermionic systems. Finally, they apply the antisymmetric sparse grid discretization to the electronic Schrödinger equation and compare costs, accuracy, convergence rates and scalability with respect to the number of electrons present in the system.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81V25 Other elementary particle theory in quantum theory
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35Q40 PDEs in connection with quantum mechanics

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References:

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