Related papers: Quantifying discretization errors for soft-tissue …
In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE)…
We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…
(Abridged) We investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These {\it finite support} (FS) effects are modelled for several estimators, simulation box sizes and source…
Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physics-informed neural networks fundamentally depart from this…
Modeling and manufacturing of personalized cranial implants are important research areas that may decrease the waiting time for patients suffering from cranial damage. The modeling of personalized implants may be partially automated by the…
A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…
Rigorous assessment of uncertainty is crucial to the utility of DNS results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier-Stokes equations. Due to the…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
Numerical simulation of the complex plasma dynamics associated with high power, high frequency microwave breakdown at high pressures, leading to the formation of filamentary plasma structures such as self-organized plasma arrays, is a…
In recent years, multicalibration has emerged as a desirable learning objective for ensuring that a predictor is calibrated across a rich collection of overlapping subpopulations. Existing approaches typically achieve multicalibration by…
In this work is considered an elliptic problem, referred to as the Ventcel problem, involvinga second order term on the domain boundary (the Laplace-Beltrami operator). A variationalformulation of the Ventcel problem is studied, leading to…
Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to…
Neurosurgery interventions involve complex tracking systems because a tissue deformation takesplace. The neuronavigation system relies only on preoperative images. In order to overcome the soft tissue deformations and guarantee the accuracy…
In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…
This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necessarily conforming to the boundaries/interfaces of the…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation…
We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…