Related papers: MIKA: a multigrid-based program package for electr…
A general real-space multigrid algorithm for the self-consistent solution of the Kohn-Sham equations appearing in the state-of-the-art electronic-structure calculations is described. The most important part of the method is the multigrid…
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…
We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent…
We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in…
We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…
Quantum linear system algorithms (QLSAs) can provide exponential speedups for the solution of linear systems, but the growth of the condition number for finite element problems can eliminate the exponential speedup. QLSAs are also incapable…
We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on…
We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve…
An algorithm for generating optimal nonuniform grids for solving the two-body Schr\"odinger equation is developed and implemented. The shape of the grid is optimized to accurately reproduce the low-energy part of the spectrum of the…
Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve…
We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from…
The Method of Invariant Grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [1-4]. Important role, in that method, is played by the initial grid which,…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead…
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…
We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…