Analytic Eigensystems for Isotropic Membrane Energies

08/15/2020
by   Julian Panetta, et al.
0

We extend the approach of [Smith et al. 2019] to derive analytical expressions for the eigenvalues and eigenmatrices of an isotropic membrane energy density function ψ : ℝ^3x2→ℝ. Clamping the eigenvalue expressions to be positive for each quadrature point of a finite element membrane simulation guarantees a positive semi-definite Hessian for the full discrete membrane energy, enabling an efficient Newton-type simulation.

READ FULL TEXT
research
08/18/2023

Fast and stable Gauss-Newton optimization of IPC barrier energy

Barrier terms for Incremental Potential Contact (IPC) energy are crucial...
research
08/01/2022

Semi-convergence of the APSS method for a class of nonsymmetric three-by-three singular saddle point problems

For nonsymmetric block three-by-three singular saddle point problems ari...
research
03/15/2021

Eigen Space of Mesh Distortion Energy Hessian

Mesh distortion optimization is a popular research topic and has wide ra...
research
12/01/2020

Bifurcation Analysis of the Eigenstructure of the Discrete Single-curl Operator in Three-dimensional Maxwell's Equations with Pasteur Media

This paper focuses on studying the bifurcation analysis of the eigenstru...
research
03/01/2019

Trajectory convergence from coordinate-wise decrease of quadratic energy functions, and applications to platoons

We consider trajectories where the sign of the derivative of each entry ...
research
04/18/2023

The conditional DPP approach to random matrix distributions

We present the conditional determinantal point process (DPP) approach to...
research
04/01/2021

On Generalizing Trace Minimization

Ky Fan's trace minimization principle is extended along the line of the ...

Please sign up or login with your details

Forgot password? Click here to reset