Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Fast and memory efficient polygonal simplification
Proceedings of the conference on Visualization '98
Adaptive Methods for Partial Differential Equations
Adaptive Methods for Partial Differential Equations
Adaptive Computational Methods for Partial Differential Equations
Adaptive Computational Methods for Partial Differential Equations
Evaluation of Memoryless Simplification
IEEE Transactions on Visualization and Computer Graphics
Level of Detail for 3D Graphics
Level of Detail for 3D Graphics
Discrete exterior calculus
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation
SIAM Journal on Numerical Analysis
Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications
Algebraic multigrid for discrete differential forms
Algebraic multigrid for discrete differential forms
A dynamic data structure for flexible molecular maintenance and informatics
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Fast Molecular Solvation Energetics and Forces Computation
SIAM Journal on Scientific Computing
| Hi-index | 0.00 |
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 guide the reduction process is chosen independent of the function the end user aims to calculate, analyze, or adaptively refine. In this paper, we argue that such a decoupling of structure from function modeling is often unwise as small changes in geometry may cause large changes in the associated function. A stable approach to mesh decimation, therefore, ought to be guided primarily by an analysis of functional sensitivity, a property dependent on both the particular application and the equations used for computation (e.g. integrals, derivatives, or integral/partial differential equations). We present a methodology to elucidate the geometric sensitivity of functionals via two major functional discretization techniques: Galerkin finite element and discrete exterior calculus. A number of examples are given to illustrate the methodology and provide numerical examples to further substantiate our choices.