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Contact forces introduce discontinuities into robot dynamics that severely limit the use of simulators for gradient-based optimization. Penalty-based simulators such as MuJoCo, soften contact resolution to enable gradient computation.…
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…
We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
We present a differentiable formulation of rigid-body contact dynamics for objects and robots represented as compositions of convex primitives. Existing optimization-based approaches simulating contact between convex primitives rely on a…
We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…
Contact involving soft materials often combines dry adhesion, sliding friction, and large deformations. At the local level, these three aspects are rarely captured simultaneously, but included in the theoretical models by Mergel et al.…
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…
In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
This paper investigates a framework (CATCH-FORM-3D) for the precise contact force control and surface deformation regulation in viscoelastic material manipulation. A partial differential equation (PDE) is proposed to model the…
In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…
Over the past few years, robotics simulators have largely improved in efficiency and scalability, enabling them to generate years of simulated data in a few hours. Yet, efficiently and accurately computing the simulation derivatives remains…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
We introduce a coupled system of PDEs for the modeling of the fluid-fluid and fluid-solid interaction in a poroelastic material with a single static fracture. The fluid flow in the fracture is modeled by a lower-dimensional Darcy equation,…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…
The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…