scholarly journals A geometric formulation of linear elasticity based on discrete exterior calculus

2021 ◽  
pp. 111345
Author(s):  
Pieter D. Boom ◽  
Odysseas Kosmas ◽  
Lee Margetts ◽  
Andrey Jivkov
Keyword(s):  
Linear Elasticity ◽  
Discrete Exterior Calculus ◽  
Exterior Calculus ◽  
Geometric Formulation

Challenges in Blood Flow Simulation: Numerical Methods and Image Processing Tools

2013 ◽  
Author(s):  
Andrea Dziubek ◽  
Edmond Rusjan ◽  
Bill Thistleton
Keyword(s):  
Blood Flow ◽  
Numerical Methods ◽  
Flow Simulation ◽  
Ocular Blood Flow ◽  
Curved Surfaces ◽  
Vascular Tree ◽  
Discrete Exterior Calculus ◽  
Exterior Calculus ◽  
Front End ◽  
Segmentation Methods

We report on recent results in modeling ocular blood flow (some parts were presented at ARVO 2013 [1]). For this simulations we used discrete exterior calculus based numerical methods. These methods aim to preserve the main features of the original analytical equations and are very suitable for curved surfaces. We will discuss the model and present the numerical methods. We will also give an overview of existing/available segmentation methods to extract the vascular tree from given retina images and our plans how to use them as a front end to our model.

Mimetic Interpolation of Vector Fields on Arakawa C/D Grids

2019 ◽  
Vol 147 (1) ◽  
pp. 3-16
Author(s):  
Alexander Pletzer ◽  
Wolfgang Hayek
Keyword(s):  
Finite Element ◽  
Vector Fields ◽  
Total Flux ◽  
Machine Accuracy ◽  
Weighted Interpolation ◽  
Discretization Methods ◽  
Finite Element Exterior Calculus ◽  
Interpolation Methods ◽  
Discrete Exterior Calculus ◽  
Exterior Calculus

Interpolation methods for vector fields whose components are staggered on horizontal Arakawa C or D grids are presented. The interpolation methods extend bilinear and area-weighted interpolation, which are widely used in Earth sciences, to work with vector fields (essentially discretized versions of differential 1-forms and 2-forms). The interpolation methods, which conserve the total flux and enforce Stokes’ theorem to near-machine accuracy, are a natural complement to discrete exterior calculus and finite element exterior calculus discretization methods.

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