Related papers: An adaptive aggregation based domain decomposition…
We describe an adaptive multigrid algorithm for solving inverses of the domain-wall fermion operator. Our multigrid algorithm uses an adaptive projection of near-null vectors of the domain-wall operator onto coarser four-dimensional…
Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this construction was mostly achieved using non-assembled matrices…
Different recently developed Krylov space methods for solving linear systems are studied and compared for the solution of the Dirac equation on the lattice. Stabilized Biconjugate Gradient (BiCGstab2) is shown to be a robust and efficient…
In this paper, the elliptic PDE-constrained optimization problem with box constraints on the control is studied. To numerically solve the problem, we apply the 'optimize-discretize-optimize' strategy. Specifically, the alternating direction…
Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…
This paper proposes a multilevel sampling algorithm for fiber sampling problems in algebraic statistics, inspired by Henry Wynn's suggestion to adapt multilevel Monte Carlo (MLMC) ideas to discrete models. Focusing on log-linear models, we…
The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present iterative Krylov subspace approximations, with deflation of critical…
This paper presents a novel approach to enhance Model Predictive Control (MPC) for legged robots through Distributed Optimization. Our method focuses on decomposing the robot dynamics into smaller, parallelizable subsystems, and utilizing…
High-order Discontinuous Galerkin (DG) methods promise to be an excellent discretisation paradigm for partial differential equation solvers by combining high arithmetic intensity with localised data access. They also facilitate dynamic…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…
Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of…
In the last few years it has been proposed a one-dimensional factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a block-local action of the auxiliary bosonic fields. Here we propose a…
Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
The discretization of elliptic PDEs leads to large coupled systems of equations. Domain decomposition methods (DDMs) are one approach to the solution of these systems, and can split the problem in a way that allows for parallel computing.…
Applying domain decomposition to the lattice Dirac operator and the associated quark propagator, we arrive at expressions which, with the proper insertion of random sources therein, can provide improvement to the estimation of the…
In this paper, we propose an efficient two-level additive Schwarz method for solving large-scale eigenvalue problems arising from the finite element discretization of symmetric elliptic operators, which may compute efficiently more interior…
We present a parallelizable SSOR preconditioning scheme for Krylov subspace iterative solvers which proves to be efficient in lattice QCD applications involving Wilson fermions. Our preconditioner is based on a locally lexicographic…
In lattice QCD the calculation of disconnected quark loops from the trace of the inverse quark matrix has large noise variance. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials on a…
We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…