Related papers: Adaptive Aggregation-based Domain Decomposition Mu…
The bulk power grid is divided into regional grids interconnected with multiple tie-lines for efficient operation. Since interconnected power grids are operated by different control centers, it is a challenging task to realize coordinated…
In this paper, we propose two novel Robin-type domain decomposition methods based on the two-grid techniques for the coupled Stokes-Darcy system. Our schemes firstly adopt the existing Robin-type domain decomposition algorithm to obtain the…
Adaptive multi-grid methods have proven very successful in dealing with critical slow down for the Wilson-Dirac solver in lattice gauge theory. Multi-grid algorithms developed for Staggered fermions using the K\"ahler-Dirac…
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that…
The advantages of using Multi-Step corrections for simulations of lattice gauge theories with dynamical fermions will be discussed. This technique is suited for algorithms based on the Multi-Boson representation of the dynamical fermions as…
I review recent theoretical developments and numerical results of twisted mass QCD. I argue that, combined with an efficient algorithm, twisted mass QCD can be an attractive QCD lattice action, to perform large scale simulations at small…
A number of proposed extensions of the Standard Model include new strongly interacting dynamics, in the form of SU(N) gauge fields coupled to various numbers of fermions. Often, these extensions allow N = 3 as a plausible choice, or even…
The paper investigates the complex gradient descent method (CGD) for the best rational approximation of a given order to a function in the Hardy space on the unit disk. It is equivalent to finding the best Blaschke form with free poles. The…
Four adaptations of the smoothed aggregation algebraic multigrid (SA-AMG) method are proposed with an eye towards improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak…
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…
Federated Learning is a popular distributed learning paradigm in machine learning. Meanwhile, composition optimization is an effective hierarchical learning model, which appears in many machine learning applications such as meta learning…
This review gives an overview on the research of algorithms for dynamical fermions used in large scale lattice QCD simulations. First a short overview on the state-of-the-art of ensemble generation at the physical point is given. Followed…
In this work we extend the shifted Laplacian approach to the elastic Helmholtz equation. The shifted Laplacian multigrid method is a common preconditioning approach for the discretized acoustic Helmholtz equation. In some cases, like…
We study a variant of the Schwarz-preconditioned HMC algorithm. In contrast to the original proposal of L\"uscher, we apply the domain decomposition in one lattice direction only. This is sufficient to reduce the condition number of the…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…
In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other methods that try to select the best…
I will review recent developments in matrix deflation methods, by Ronald Morgan/Walter Wilcox, Andreas Stathopoulos/Konstantinos Orginos, and Martin L\"uscher, with application to lattice QCD fermion inversion. I will begin with a short…
We study the properties of pions in twisted mass lattice QCD (with two degenerate flavors) using chiral perturbation theory (ChPT). We work to next-to-leading order (NLO) in a power counting scheme in which m_q ~ a \Lambda_QCD^2, with m_q…