Related papers: A novel multigrid method for electronic structure …
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
We introduce a hybrid approach to applying the density matrix renormalization group (DMRG) to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set along the remaining two directions. This…
Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…
From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
Numerical simulations of quantum chromodynamics (QCD) on a lattice require the frequent solution of linear systems of equations with large, sparse and typically ill-conditioned matrices. Algebraic multigrid methods are meanwhile the…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…
Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the…
This paper provides a unified and detailed presentation of root-node style algebraic multigrid (AMG). Algebraic multigrid is a popular and effective iterative method for solving large, sparse linear systems that arise from discretizing…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence…
We present evidence that multigrid (MG) works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder. We introduce a "neural computations" point of view into large scale…
Fundamental theories and practical methods for large-scale electronic structure calculations are given, in which the computational cost is proportional to the system size. Accuracy controlling methods for microscopic freedoms are focused on…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and…
Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…
Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…
The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schroedinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed…