Related papers: A Generalized Solution Method for Parallelized Com…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation…
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…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
We generalize the hyper-systolic algorithm proposed in [1] for abstract data structures on massive parallel computers with $n_p$ processors. For a problem of size $V$ the communication complexity of the hyper-systolic algorithm is…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
The Poisson equation governing a planet's gravitational field is posed on the unbounded domain, $\mathbb{R}^3$, whereas finite-element computations require bounded meshes. We implement and compare three strategies for handling the infinite…
Modeling of collisionless galactic systems is based on the N-body model, which requires large computational resources due to the long-range nature of gravitational forces. The most common method for calculating gravity is the TreeCode…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system to the gravitational potential and others (kinetic and internal energies) and…
We describe a generic infrastructure for time evolution simulations in numerical relativity using multiple grid patches. After a motivation of this approach, we discuss the relative advantages of global and patch-local tensor bases. We…
In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method from [Crane et al. 2013] can be reformulated…
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.…