Related papers: Fourier-based schemes for computing the mechanical…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations…
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
We present an explicit second order staggered finite difference (FD) discretization scheme for forward simulation of natural gas transport in pipeline networks. By construction, this discretization approach guarantees that the conservation…
Modern processors deliver higher throughput for lower-precision arithmetic than for higher-precision arithmetic. For matrix multiplication, the Ozaki scheme exploits this performance gap by splitting the inputs into lower-precision…
Fast, high-order accurate algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied…
The paper develops a novel design optimization framework and associated computational techniques for staged deployment optimization of complex systems under operational uncertainties. It proposes a local scenario discretization method that…
A new discretisation scheme for the gradient operator, suitable for use in second-order accurate Finite Volume Methods (FVMs), is proposed. The derivation of this scheme, which we call the Taylor-Gauss (TG) gradient, is similar to that of…
In this paper, we assess the performance of four iterative algorithms for solving non-symmetric rank-deficient linear systems arising in the FFT-based homogenization of heterogeneous materials defined by digital images. Our framework is…
We present a new method to accelerate real time-time dependent density functional theory (rt-TDDFT) calculations with hybrid exchange-correlation functionals. For large basis set, the computational bottleneck for large scale calculations is…
The inaccuracy of the classical magnetic field integral equation (MFIE) is a long-studied problem. We investigate one of the potential approaches to solve the accuracy problem: higher-order discretization schemes. While these are able to…
We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly increase as we move away from the Black-Scholes-Merton framework. We rank the…
A higher-order numerical method is presented for scalar valued, coupled forward-backward stochastic differential equations. Unlike most classical references, the forward component is not only discretized by an Euler-Maruyama approximation…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
A general local Fourier analysis for overlapping block smoothers on triangular grids is presented. This analysis is explained in a general form for its application to problems with different discretizations. This tool is demonstrated for…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
An approach is proposed to improve the efficiency of fourth-order algorithms for numerical integration of the equations of motion in molecular dynamics simulations. The approach is based on an extension of the decomposition scheme by…
The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to compute a divergence free velocity. The non-conforming Crouzeix-Raviart finite element are convenient since they…