A Finite-Element Approach to the Poisson Equation for Large-Scale Electronic Structure Calculations
Abstract
We report our progress on a finite-element (FE)-based approach for large-scale electronic structure calculations. We have previously reported upon our FE-based approach to the solution of the Schroedinger equation [1,2] and here report initial results for the Poisson Equation. The finite-element basis consists of strictly local, piecewise polynomials. Because the basis functions are polynomial in nature, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well-suited to parallel implementation. We show results illustrating the accuracy, convergence, and scaling of the method in the context of a triclinic model charge density and Si pseudo-charge density. It will be seen that the method converges at the maximum possible rate consistent with the completeness of the basis, both pointwise and in the L^2 norm, and that it scales strictly linearly with system size. [1] Phys. Rev. B 59, 12352 (1999). [2] Appl. Surf. Sci. 149, 238 (1999).
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 2000
- Bibcode:
- 2000APS..MARB16005P