Rigorous shape derivative of eigenvalues estimation (alpha version)
First version: 2022/08/24
- The codes run on latest MATLAB environment along with INTLAB toolbox (http://www.ti3.tu-harburg.de/rump/intlab/).
- Since Octave does not supply ldl function for indefinite symmetric matrix, the rigorous evaluation is not available for Octave.
Edit my_intlab_mode_config.m to configure the computing environment.
%The path of INTLAB toolbox and initialization. addpath('Intlab_V9') %The path of the library of verified eigenvalue estimation for matrix. addpath('verified_eig_estimation') %The path of the codes for switch between verified computing and approximate computing. addpath('mode_swith_interface') %The path of the library of FEMs on triangular domains addpath('functions') startintlab; global INTERVAL_MODE; %The value can be 0 or 1. See readme.md %INTERVAL_MODE=1; for rigorous computing based on interval arithmetic. %INTERVAL_MODE=0; for approximate computing with rounding error inside. INTERVAL_MODE=1;
Remeber to run "my_intlab_mode_config" before other codes.
How to use it?
For the purpose of rigorous computation, please run the code in MATLAB along with the INTLAB toolbox.
The code has two running mode: approximate evaluation and verified evaluation.
To swith between each other, please set the value of INTERVAL_MODE.
- INTERVAL_MODE=0: approximate computation mode.
- INTERVAL_MODE=1: verified computation mode. It takes longer time that approximate computation mode. So be careful with the mesh size, which should not be too small.
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