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This work presents a Discrete de Rham (DDR) numerical scheme for solving linear elasticity problems on general polyhedral meshes, with a focus on preventing volumetric locking in the quasi-incompressible regime. The method is formulated as…
Protein flexibility is crucial for understanding protein structures, functions, and dynamics, and it can be measured through experimental methods such as X-ray crystallography. Theoretical approaches have also been developed to predict…
Autonomous wire harness assembly requires robots to manipulate complex branched cables with high precision and reliability. A key challenge in automating this process is predicting how these flexible and branched structures behave under…
Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…
Dislocations are the carriers of plasticity in crystalline materials. Their collective interaction behavior is dependent on the strain rate and sample size. In small specimens, details of the nucleation process are of particular importance.…
In this work, we aim to teach robots to manipulate various thin-shell materials. Prior works studying thin-shell object manipulation mostly rely on heuristic policies or learn policies from real-world video demonstrations, and only focus on…
Design of robots at the small scale is a trial-and-error based process, which is costly and time-consuming. There are few dynamic simulation tools available to accurately predict the motion or performance of untethered microrobots as they…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may…
Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to…
Scientific computing for large deformation of elastic-plastic solids is critical for numerous real-world applications. Classical numerical solvers rely primarily on local discrete linear approximation and are constrained by an inherent…
The simulation of partial differential equations is a central subject of numerical analysis and an indispensable tool in science, engineering and related fields. Existing approaches, such as finite elements, provide (highly) efficient tools…
A discontinuous Petrov-Galerkin (DPG) method is used to solve the time-harmonic equations of linear viscoelasticity. It is based on a "broken" primal variational formulation, which is very similar to the classical primal variational…
This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology. Ultraweak variational formulations are nonstandard in…
We propose DynamicSurf, a model-free neural implicit surface reconstruction method for high-fidelity 3D modelling of non-rigid surfaces from monocular RGB-D video. To cope with the lack of multi-view cues in monocular sequences of deforming…
In this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomial on the mesh…
The prediction of upcoming events in industrial processes has been a long-standing research goal since it enables optimization of manufacturing parameters, planning of equipment maintenance and more importantly prediction and eventually…
A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite…
Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical…
A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in our previous computational work. This paper presents a numerical…