Related papers: A Task Parallel Orthonormalization Multigrid Metho…
We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem and we propose multigrid methods to solve the discretized system. We prove that the $W$-cycle algorithm is uniformly convergent in the energy…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
The problem of finding the solution of Partial Differential Equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of $hp$-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in…
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…
Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a Partial Differential Equation (PDE), providing possibilities for accelerating the computation of its solution. While parallelisation in time has…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
We present an overview of randomized orthogonalization techniques that construct a well-conditioned basis whose sketch is orthonormal. Randomized orthogonalization has recently emerged as a powerful paradigm for reducing the computational…
Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to…
Cholesky factorization is a widely used method for solving linear systems involving symmetric, positive-definite matrices, and can be an attractive choice in applications where a high degree of numerical stability is needed. One such…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine…
Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous…
As CPU clock speeds have stagnated, and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes are a…
Asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and…
In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple…
Multigrid algorithms are among the fastest iterative methods known today for solving large linear and some non-linear systems of equations. Greatly optimized for serial operation, they still have a great potential for parallelism not fully…