Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly in... more Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each
ABSTRACT This paper presents two methods based on domain decomposition concepts for determining t... more ABSTRACT This paper presents two methods based on domain decomposition concepts for determining the diagonal of the inverse of specific matrices. The first uses a divide-and-conquer principle and the Sherman-Morrison-Woodbury formula and assumes that the matrix can be decomposed into a $2 \times 2$ block-diagonal matrix and a low-rank matrix. The second method is a standard domain decomposition approach in which local solves are combined with a global correction. Both methods can be successfully combined with iterative solvers and sparse approximation techniques. The efficiency of the methods usually depends on the specific implementation, which should be fine-tuned for different test problems. Preliminary results for some two-dimensional (2D) problems are reported to illustrate the proposed methods.
... for Bubbly Flow Problems Jok Man Tang and Kees Vuik ... Sousa, FS, Mangiavacchi, N., Nonato, ... more ... for Bubbly Flow Problems Jok Man Tang and Kees Vuik ... Sousa, FS, Mangiavacchi, N., Nonato, LG, Castelo, A., Tome, MF, Ferreira, VG, Cuminato, JA, McKee, S.: A Front-Tracking / Front-Capturing Method for the Simulation of 3D Multi-Fluid Flows with Free Surfaces. J. Comp. ...
Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly in... more Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each
ABSTRACT This paper presents two methods based on domain decomposition concepts for determining t... more ABSTRACT This paper presents two methods based on domain decomposition concepts for determining the diagonal of the inverse of specific matrices. The first uses a divide-and-conquer principle and the Sherman-Morrison-Woodbury formula and assumes that the matrix can be decomposed into a $2 \times 2$ block-diagonal matrix and a low-rank matrix. The second method is a standard domain decomposition approach in which local solves are combined with a global correction. Both methods can be successfully combined with iterative solvers and sparse approximation techniques. The efficiency of the methods usually depends on the specific implementation, which should be fine-tuned for different test problems. Preliminary results for some two-dimensional (2D) problems are reported to illustrate the proposed methods.
... for Bubbly Flow Problems Jok Man Tang and Kees Vuik ... Sousa, FS, Mangiavacchi, N., Nonato, ... more ... for Bubbly Flow Problems Jok Man Tang and Kees Vuik ... Sousa, FS, Mangiavacchi, N., Nonato, LG, Castelo, A., Tome, MF, Ferreira, VG, Cuminato, JA, McKee, S.: A Front-Tracking / Front-Capturing Method for the Simulation of 3D Multi-Fluid Flows with Free Surfaces. J. Comp. ...
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