Related papers: A Butterfly-Based Direct Integral Equation Solver …
Algorithmic and architecture-oriented optimizations are essential for achieving performance worthy of anticipated energy-austere exascale systems. In this paper, we present an extreme scale FMM-accelerated boundary integral equation solver…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
We evaluate the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations. The methods are based on affine combinations of time-splitting integrators and…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
We consider space-efficient single-pass estimation of the number of butterflies, a fundamental bipartite graph motif, from a massive bipartite graph stream where each edge represents a connection between entities in two different…
Fast Fourier transform (FFT) of large number of samples requires huge hardware resources of field programmable gate arrays (FPGA), which needs more area and power. In this paper, we present an area efficient architecture of FFT processor…
Study of general purpose computation by GPU (Graphics Processing Unit) can improve the image processing capability of micro-computer system. This paper studies the parallelism of the different stages of decimation in time radix 2 FFT…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and…
We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the…
High-fidelity flow simulations are indispensable when analyzing systems exhibiting multiphase flow phenomena. The accuracy of multiphase flow simulations is strongly contingent upon the finest mesh resolution used to represent the…
The Electric Field Integral Equation (EFIE) is a well-established tool to solve electromagnetic scattering problems. However, the development of efficient and easy to implement preconditioners remains an active research area. In recent…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
We introduce a Monte Carlo integration-based Shooting and Bouncing Ray (SBR) algorithm for electromagnetic scattering, specifically targeting complex dielectric materials. Unlike traditional deterministic SBR methods, our approach is the…
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…
For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…
Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several…
Writing high performance solvers for engineering applications is a delicate task. These codes are often developed on an application to application basis, highly optimized to solve a certain problem. Here, we present our work on developing a…
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…