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This paper introduces a new accurate model for periodic fractional optimal control problems (PFOCPs) using Riemann-Liouville (RL) and Caputo fractional derivatives (FDs) with sliding fixed memory lengths. The paper also provides a novel…
We describe a parallel algorithm for solving the time-independent 3d Schrodinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between…
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…
Time fractional PDEs have been used in many applications for modeling and simulations. Many of these applications are multiscale and contain high contrast variations in the media properties. It requires very small time step size to perform…
We study the probability and energy conservation properties of a leap-frog finite-difference time-domain (FDTD) method for solving the Schr\"odinger equation. We propose expressions for the total numerical probability and energy contained…
We present the implementation and application of a multiphysics simulation technique to carrier dynamics under electromagnetic excitation in supported two-dimensional electronic systems. The technique combines ensemble Monte Carlo (EMC) for…
Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient-specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems, but need…
PUBLISHED ON IEEE/ASME TRANSACTIONS ON MECHATRONICS, DOI: 10.1109/TMECH.2021.3100150. Ideally, accurate sensor measurements are needed to achieve a good performance in the closed-loop control of mechatronic systems. As a consequence, sensor…
A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate. We prove…
To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex…
Dynamical properties are studied numerically for a variant of the Kondo model with singlet and triplet crystalline electric field (CEF) levels where Kondo and CEF singlets compete for the ground state. Using the continuous-time quantum…
A face-centred finite volume (FCFV) method is proposed for the linear elasticity equation. The FCFV is a mixed hybrid formulation, featuring a system of first-order equations, that defines the unknowns on the faces (edges in two dimensions)…
Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…
Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…
An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…
The properties of liquid crystals can be modelled using an order parameter which describes the variability of the local orientation of rod-like molecules. Defects in the director field can arise due to external factors such as applied…
This paper concerns the numerical solution of three-dimensional degenerate Kawarada equations. These partial differential equations possess highly nonlinear source terms, and exhibit strong quenching singularities which pose severe…
The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics",…
A procedure for largely suppressing the numerical Cherenkov instability in finite difference time-domain (FDTD) particle-in-cell (PIC) simulations of cold, relativistic beams is derived, and residual growth rates computed and compared with…
A new implicit-explicit local differential transform method (IELDTM) is derived here for time integration of the nonlinear advection-diffusion processes represented by (2+1)-dimensional Burgers equation. The IELDTM is adaptively constructed…