Related papers: Delayed approximate matrix assembly in multigrid w…
For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…
We introduce a family of implementations of low order, additive, geometric multilevel solvers for systems of Helmholtz equations. Both grid spacing and arithmetics may comprise complex numbers and we thus can apply complex scaling…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…
Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…
An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…
Algebraic multigrid (AMG) is one of the fastest numerical methods for solving large sparse linear systems. For SPD matrices, convergence of AMG is well motivated in the $A$-norm, and AMG has proven to be an effective solver for many…
Handling the ever-increasing complexity of mesh generation codes along with the intricacies of newer hardware often results in codes that are both difficult to comprehend and maintain. Different facets of codes such as thread management and…
Dedicated hardware accelerators are suitable for parallel computational tasks. Moreover, they have the tendency to accept inexact results. These hardware accelerators are extensively used in image processing and computer vision…
Self-assembly processes in biological and synthetic biomolecular systems are often governed by the spatial separation of biochemical processes. While previous work has focused on optimizing self-assembly through fine-tuned reaction…
We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…
In matching markets such as kidney exchanges and freight exchanges, delayed matching has been shown to improve overall market efficiency. The benefits of delay are highly sensitive to participants' sojourn times and departure behavior, and…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
The development of deep learning architectures is a resource-demanding process, due to a vast design space, long prototyping times, and high compute costs associated with at-scale model training and evaluation. We set out to simplify this…
Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix…
Multivariate time series alignment is critical for ensuring coherent analysis across variables, but missing values and timestamp inconsistencies make this task highly challenging. Existing approaches often rely on prior imputation, which…