Related papers: A Stable FDTD Method with Embedded Reduced-Order M…
Recent advances in generative modeling with diffusion processes (DPs) enabled breakthroughs in image synthesis. Despite impressive image quality, these models have various prompt compliance problems, including low recall in generating…
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…
Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve…
We proposed a provably stable FDTD subgridding method for accurate and efficient transient electromagnetic analysis. In the proposed method, several field components are properly added to the boundaries of Yee's grid to make sure that the…
Federated Learning (FL) is a promising distributed machine learning approach that enables collaborative training of a global model using multiple edge devices. The data distributed among the edge devices is highly heterogeneous. Thus, FL…
The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…
Finite-difference time-domain (FDTD) simulations often involve physical quantities spanning multiple orders of magnitude, such as the speed of light or electromagnetic field amplitudes. The standard practice for maintaining numerical…
Masked diffusion models (MDMs) have recently emerged as a promising alternative to autoregressive models over discrete domains. MDMs generate sequences in an any-order, parallel fashion, enabling fast inference and strong performance on…
This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of…
A finite-difference time-domain (FDTD) modelling of finite-size zero thickness space-time modulated Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and numerically demonstrated. A typical…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…
Despite the recent visually-pleasing results achieved, the massive computational cost has been a long-standing flaw for diffusion probabilistic models (DPMs), which, in turn, greatly limits their applications on resource-limited platforms.…
Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
Federated learning (FL), as a collaborative distributed training paradigm with several edge computing devices under the coordination of a centralized server, is plagued by inconsistent local stationary points due to the heterogeneity of the…
Alternative unsplit-filed-based absorbing boundary condition (ABC) computation approach for the finite-difference time-domain (FDTD) is efficiently proposed based on the deep differentiable forest. The deep differentiable forest (DDF) model…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
Standard finite element methods employ an element-wise assembly strategy. The element's contribution to the system matrix is formed by a loop over quadrature points. This concept is also used in fictitious domain methods, which perform…
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…