Related papers: Efficient simulation of DC-DC switch-mode power co…
The multipole-expansion (MPE) model is an implicit solvation model used to efficiently incorporate solvent effects in quantum chemistry. Even within the recent direct approach, the multipole basis used in MPE to express the dielectric…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
Finding the general solution of partial differential equations (PDEs) is essential for controller design in newly developed methods. Interconnection and damping assignment passivity based control (IDA-PBC) is one of such methods in which…
Modeling power electronic converters at frequencies close to or above half the switching frequency has been difficult due to the time-variant and discontinuous switching actions. This paper uses the properties of moving Fourier coefficients…
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…
Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…
Harmonic instability occurs frequently in the power electronic converter system. This paper leverages multi-resolution dynamic mode decomposition (MR-DMD) as a data-driven diagnostic tool for the system stability of power electronic…
Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as finite element methods, with solutions over the…
We present a priori error estimates for a multirate time-stepping scheme for coupled differential equations. The discretization is based on Galerkin methods in time using two different time meshes for two parts of the problem. We aim at…
A modular and scalable converter for medium voltage (MV) AC to low voltage (LV) DC power conversion is proposed; single-phase-modules (SPMs), each consisting of an active-front-end (AFE) stage and an isolated DC-DC stage, are connected in…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
Here we consider the magnetization dynamics in ferromagnetic nanoparticles or films driven by external magnetic field pulses directed transverse to the initial equilibrium state. The excitation pulse drives large-angle ultra-fast…
Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there…
In recent years, the use of multilevel inverter has become popular due to its many advantages. Due to the popularity of multilevel inverters in industries and in applications that require a wide range of voltages, there have been many…
Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS…
Partial differential equations (PDEs) are crucial in modeling diverse phenomena across scientific disciplines, including seismic and medical imaging, computational fluid dynamics, image processing, and neural networks. Solving these PDEs at…
The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
In this paper, we investigate the fractional powers of block operator matrices, with a particular focus on their applications to partial differential equations (PDEs). We develop a comprehensive theoretical framework for defining and…