Defect corrected averaging for highly oscillatory problems

2015 ◽  
Vol 261 ◽  
pp. 90-103 ◽  
Author(s):  
A. Gerisch ◽  
A. Naumann ◽  
J. Wensch
Keyword(s):  
Highly Oscillatory ◽  
Highly Oscillatory Problems

Mini-Workshop: Fast Solvers for Highly Oscillatory Problems

2017 ◽  
Vol 13 (4) ◽  
pp. 2867-2907
Author(s):  
Timo Betcke ◽  
Steffen Börm ◽  
Sabine Le Borne ◽  
Per-Gunnar Martinsson
Keyword(s):  
Fast Solvers ◽  
Highly Oscillatory ◽  
Highly Oscillatory Problems

Hyperelasticity for crystals

1990 ◽  
Vol 1 (2) ◽  
pp. 113-129 ◽  
Author(s):  
Michel Chipot
Keyword(s):  
Energy Level ◽  
Thermodynamic Quantity ◽  
Energy Functional ◽  
Invariance Properties ◽  
Highly Oscillatory ◽  
Highly Oscillatory Problems ◽  
Relaxed Energy ◽  
Boundary Deformation

The goal of this note is to explain the process of computing the lowest energy level achieved by an elastic crystal subject to homogeneous boundary deformation. This analysis follows mainly the lines of Chipot and Kinderlehrer or Fonesca but we expect that it will lead to some new results for some other energy functional having different invariance properties. The mathematical interest of the result also lies in the fact that the lowest energy level computed this way coincides with the relaxed energy functional (see Fonesca). This relaxed energy is determined by a known thermodynamic quantity, Ericksen' subenergy. Within this review we will also analyse some of the mathematical and physical aspects of these highly oscillatory problems.

scholarly journals HOODESolver.jl: A Julia package for highly oscillatory problems

2021 ◽  
Vol 6 (61) ◽  
pp. 3077
Author(s):  
Yves Mocquard ◽  
Pierre Navaro ◽  
Nicolas Crouseilles
Keyword(s):  
Highly Oscillatory ◽  
Highly Oscillatory Problems
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