Rigorous shape derivative of eigenvalues estimation




This project demonstrates an implementation of the algorithms proposed in "Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error constant estimation".



  • DEMO

Rigorous shape derivative of eigenvalues estimation (alpha version)

Ryoki ENDO

First version: 2022/08/24

Running environment

  • 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.

%The path of the library of verified eigenvalue estimation for matrix.

%The path of the codes for switch between verified computing and approximate computing.

%The path of the library of FEMs on triangular domains

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.

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.

About the directory

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