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We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs,…
Recently, near-field radiative heat transfer enhancement across nanometer vacuum gaps has been intensively studied between two hyperbolic metamaterials (HMMs) due to unlimited wavevectors and high photonic density of state. In this work, we…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
We present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). The image registration framework…
In recent decades, the study of fracture propagation in solids has increasingly relied on phase-field models. Several recent contributions have highlighted the potential of this approach in both static and dynamic frameworks. However, a…
This study was undertaken to develop a system for heat transfer simulation for optimization and treatment planning of magnetic hyperthermia treatment (MHT) using magnetic particle imaging (MPI). First, we performed phantom experiments to…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
Multi-fidelity (MF) methods are gaining popularity for enhancing surrogate modeling and design optimization by incorporating data from various low-fidelity (LF) models. While most existing MF methods assume a fixed dataset, adaptive…
This work expands on our recently introduced low Mach enthalpy method [1] for simulating the melting and solidification of a phase change material (PCM) alongside (or without) an ambient gas phase. The method captures PCM's volume change…
A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
Shaping thermoplastic sheets into three-dimensional products is challenging since overheating results in failed manufactured parts and wasted material. To this end, we propose an indirect data-driven predictive control approach using Model…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
In this manuscript, we introduce a tensor-based approach to Non-Negative Tensor Factorization (NTF). The method entails tensor dimension reduction through the utilization of the Einstein product. To maintain the regularity and sparsity of…
The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient algorithm for addressing the numerical sign problem at moderate computational cost. It mitigates the sign problem while avoiding the ergodicity issues…