A boundary value problem arising from nonlinear viscoelasticity: Mathematical analysis and numerical simulations

2018 ◽  
Vol 335 ◽  
pp. 237-247
Author(s):  
R. Cipolatti ◽  
I.-S. Liu ◽  
L.A. Palermo ◽  
M.A. Rincon ◽  
R.M.S. Rosa
Keyword(s):  
Boundary Value Problem ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Nonlinear Viscoelasticity ◽  
Boundary Value

Influence of Timestep and Mesh Sizes on Numerical Simulations of Boundary Value Problem Model of Electrostatically Actuated MEMS Resonators

2019 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Boundary Value Problem ◽  
Numerical Simulations ◽  
Multiple Scales ◽  
Boundary Value ◽  
Mesh Size ◽  
Problem Solver ◽  
Time Step ◽  
Problem Model ◽  
Electrostatically Actuated ◽  
Mems Resonators

Abstract This paper deals with the effects of mesh size and time step on the numerical simulations using bvp4c, a Matlab Boundary Value Problem solver, on the time response of electrostatically actuated MEMS resonators. These results are compared to the reduced order model as well as the method of multiple scales to test how accurate these results are at lower amplitudes. The refinement of mesh size leads to more accurate results to a certain extent, as it eventually reaches a convergence. It should be said that the larger the mesh size, the longer the calculations take. A similar result occurs with timestep size. The smaller the timestep the more accurate the results. However, the CPU time increases significantly. However, beyond a certain timestep, any smaller time step would not yield any noticeable differences. Thus it can be said convergence has been reached.

Matched Asymptotic Expansions of the Eigenvalues of a 3-D Boundary-Value Problem Relative to Two Cavities Linked by a Hole of Small Size

2012 ◽  
Vol 11 (2) ◽  
pp. 456-471 ◽  
Author(s):  
Abderrahmane Bendali ◽  
M’Barek Fares ◽  
Abdelkader Tizaoui ◽  
Sébastien Tordeux
Keyword(s):  
Boundary Value Problem ◽  
Numerical Simulations ◽  
Elliptic Operator ◽  
Numerical Method ◽  
Asymptotic Expansions ◽  
Convergence Rates ◽  
Boundary Value ◽  
Matched Asymptotic Expansions

AbstractIn this article, we consider a domain consisting of two cavities linked by a hole of small size. We derive a numerical method to compute an approximation of the eigenvalues of an elliptic operator without refining in the neighborhood of the hole. Several convergence rates are obtained and illustrated by numerical simulations.

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