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As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to…
Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering…
The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due…
We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are…
In this paper we rigorously prove the validity of the cavity method for the problem of counting the number of matchings in graphs with large girth. Cavity method is an important heuristic developed by statistical physicists that has lead to…
We present and experimentally verify a matrix approach for determining how to optimally sculpt an input wavefront both in space and time for any desired wave-control functionality, irrespective of the complexity of the wave scattering. We…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Nowadays, high-speed machining is usually used for production of hardened material parts with complex shapes such as dies and molds. In such parts, tool paths generated for bottom machining feature with the conventional parallel plane…
The analysis of scattering from complex objects using surface integral equations is a challenging problem. Its resolution has wide ranging applications- from crack propagation to diagnostic medicine. The two ingredients of any integral…
The aim of this paper is to describe a Matlab toolbox, called $\mu$-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in $\mu$-diff…
The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the…
We present an efficient, parallel, constrained optimization technique for approximating CAD curves with super-convergent rates. The optimization function is a disparity measure in terms of a piece-wise polynomial approximation and a curve…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
This paper introduces a shape optimisation framework for achieving desired mutual inductances (MIs) among coils in 3D space. Utilising a wire modelling approach, the coils are discretised using B-spline curves, with control points (CPs)…
Flow-matching generative models are increasingly used to simulate cell responses to biological perturbations. However, the design space for building such models is large and underexplored. We systematically analyse the design space of flow…
In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories…
Modularity is a promising approach for scaling up quantum computers and therefore integrating higher qubit counts. The essence of such architectures lies in their reliance on high-fidelity and fast quantum state transfers enabled by…