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We present a proof of concept for solving a 1+1D complex-valued, delay partial differential equation (PDE) that emerges in the study of waveguide quantum electrodynamics (QED) by adapting the finite-difference time-domain (FDTD) method. The…
The finite difference time domain (FDTD) method has been successfully applied to obtain energies and wave functions for two electrons in a quantum dot modeled by a three dimensional harmonic potential. The FDTD method uses the…
In this work, we present a numerical method that remedies the instabilities of the conventional FDTD approach for solving Maxwell's equations in a space-time dependent magneto-electric medium with direct application to the simulation of the…
A Finite-Difference Time-Domain (FDTD) scheme with Perfectly Matched Layers (PMLs) is considered for solving the time-dependent Schr\"{o}dinger equation, and simulate the ionization of an electron initially bound to a one-dimensional…
In this work, we propose staggered FDTD schemes based on the correction function method (CFM) to discretize Maxwell's equations with embedded perfect electric conductor (PEC) boundary conditions. The CFM uses a minimization procedure to…
An alternative way of visualizing electromagnetic waves in matter and of deriving the Finite Difference Time Domain method (FDTD) for simulating Maxwell's equations for one dimensional systems is presented. The method uses d'Alembert's…
The exponential growth of artificial intelligence has fueled the development of high-bandwidth photonic interconnect fabrics as a critical component of modern AI supercomputers. As the demand for ever-increasing AI compute and connectivity…
The traditional finite-difference time-domain (FDTD) method is constrained by the Courant-Friedrich-Levy (CFL) condition and suffers from the notorious staircase error in electromagnetic simulations. This paper proposes a three-dimensional…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
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…
We report the first CUDA graphics-processing-unit (GPU) implementation of the polymer field-theoretic simulation framework for determining fully fluctuating expectation values of equilibrium properties for periodic and select aperiodic…
A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwell's equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous…
Time domain simulations are crucial for analyzing transient behavior and broadband responses in electromagnetic problems. However, conventional numerical methods such as finite element method in time domain (FEMTD) and finite difference…
Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in…
A general method for numerical computation of the thermal density matrix of a single-particle quantum system is presented. The Schrodinger equation in imaginary time tau is solved numerically by the finite difference time domain (FDTD)…
A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee…
The finite-difference time-domain (FDTD) method, which is important in photonic hardware design flow, is widely adopted to solve time-domain Maxwell equations. However, FDTD is known for its prohibitive runtime cost, taking minutes to hours…
We present a Pseudo-Transient Topology Optimization (PeTTO) approach that can leverage graphics processing units (GPUs) to efficiently solve single-material and multi-material topology optimization problems. By integrating PeTTO with phase…
A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…
A conformal dispersive finite-difference time-domain (FDTD) method is developed for the study of one-dimensional (1-D) plasmonic waveguides formed by an array of periodic infinite-long silver cylinders at optical frequencies. The curved…