Related papers: Boosting the Efficiency of the Differential Algebr…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
In this article, a fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme, which aims at solving nonlinear problems quickly, is considered to numerically solve the nonlinear space fractional Allen-Cahn equations with smooth…
The factorization of skew-symmetric matrices is a critically understudied area of dense linear algebra, particularly in comparison to that of general and symmetric matrices. While some algorithms can be adapted from the symmetric case, the…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
We propose a new computational framework that combines the recently developed time-parallel (TP) and the compound wavelet matrix (CWM) methods. The framework, termed tpCWM, offers significant computational acceleration by making…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…
Automated machine learning (AutoML) can produce complex model ensembles by stacking, bagging, and boosting many individual models like trees, deep networks, and nearest neighbor estimators. While highly accurate, the resulting predictors…
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a…
Rate-splitting multiple access (RSMA) has been proven as an effective communication scheme for 5G and beyond. However, current approaches to RSMA resource management require complicated iterative algorithms, which cannot meet the stringent…
We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume potential in terms of the Green's function, we arrive at the…
Charge and energy transfer in biological and synthetic organic materials are strongly influenced by the coupling of electronic states to high-frequency underdamped vibrations under dephasing noise. Non-perturbative simulations of these…
This paper introduces an efficient algorithm for persistence diagram computation, given an input piecewise linear scalar field $f$ defined on a $d$-dimensional simplicial complex $K$, with $d \leq 3$. Our work revisits the seminal algorithm…
In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…
In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of…
Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to…
This article presents a fast direct solver, termed Algebraic Inverse Fast Multipole Method (from now on abbreviated as AIFMM), for linear systems arising out of $N$-body problems. AIFMM relies on the following three main ideas: (i) Certain…
The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist…
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…
Due to massive amounts of data distributed across multiple locations, distributed machine learning has attracted a lot of research interests. Alternating Direction Method of Multipliers (ADMM) is a powerful method of designing distributed…
Multivariate partial fractioning is a powerful tool for simplifying rational function coefficients in scattering amplitude computations. Since current research problems lead to large sets of complicated rational functions, performance of…