Related papers: Parallel FFT-based Poisson Solver for Isolated Thr…
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the…
The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few…
Although the isogeometric analysis has shown its great potential in achieving highly accurate numerical solutions of partial differential equations, its efficiency is the main factor making the method more competitive in practical…
The FFT of three-dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on a large number of processors. Performance of many scientific…
In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element…
We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with random coefficients. The algorithm is an adaption of the sparse…
We describe a new hybrid N-body/hydrodynamical code based on the particle-mesh (PM) method and the piecewise-parabolic method (PPM) for use in solving problems related to the evolution of large-scale structure, galaxy clusters, and…
Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical…
We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier-Stokes equations,…
Fast and high-order accurate algorithms for three dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
An accurate description of 2-D quantum transport in a double-gate metal oxide semiconductor filed effect transistor (dgMOSFET) requires a high-resolution solver to a coupled system of the 4-D Wigner equation and 2-D Poisson equation. In…
Recently, the deep learning method has been used for solving forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). It has good accuracy and performance for high-dimensional…
The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…
A dedicated simulator, Poisson_CCD, has been constructed which models astronomical CCDs by solving Poisson's equation numerically and simulating charge transport within the CCD. The potentials and free carrier densities within the CCD are…
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
In the field of High Performance Computing, communications among processes represent a typical bottleneck for massively parallel scientific applications. Object of this research is the development of a network interface card with specific…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…