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Shock-physics numerical codes are essential tools for describing the short but extreme fragmentation stage of the hypervelocity impact process on asteroids. However, accurately representing complex interior structures, surfaces, and contact…
The ability to accurately quantify the performance an additively manufactured (AM) product is important for a widespread industry adoption of AM as the design is required to: (1) satisfy geometrical constraints, (2) satisfy structural…
In this paper, we describe a new scalable and modular material point method (MPM) code developed for solving large-scale problems in continuum mechanics. The MPM is a hybrid Eulerian-Lagrangian approach, which uses both moving material…
Legacy software systems, written in outdated languages like MUMPS and mainframe assembly, pose challenges in efficiency, maintenance, staffing, and security. While LLMs offer promise for modernizing these systems, their ability to…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement…
We present simulations of the dynamic and temperature dependent behavior of Micro-Electro-Mechanical Systems (MEMS) by utilizing recently developed parallel codes which enable a coupling of length scales. The novel techniques used in this…
Uncertainty quantification is not yet widely adapted in the design process of engineering components despite its importance for achieving sustainable and resource-efficient structures. This is mainly due to two reasons: 1) Tracing the…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
The sources of reliable, code-level information about vulnerabilities that affect open-source software (OSS) are scarce, which hinders a broad adoption of advanced tools that provide code-level detection and assessment of vulnerable OSS…
A stationary Stokes problem with a piecewise constant viscosity coefficient in multiple subdomains is considered in the paper. For standard finite element pairs, a robust inf-sup condition is required to show the robustness of the…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
A number of recent studies have focused on developing surgical simulation platforms to train machine learning (ML) agents or models with synthetic data for surgical assistance. While existing platforms excel at tasks such as rigid body…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
Simulink is widely used in industrial design processes to model increasingly complex embedded control systems. Thus, their formal analysis is highly desirable. However, this comes with two major challenges: First, Simulink models often…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
While LLM-based specification generation is gaining traction, existing tools primarily focus on mainstream programming languages like C, Java, and even Solidity, leaving emerging and yet verification-oriented languages like Move…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…