### Title

Rigorous shape derivative of eigenvalues estimation

### Description

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".

Public

• DIRECTORY
• 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.

## Configuration

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
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.

Folders or files beginning with a dot are not displayed by default.

## Virtual Machine Setting

#### Warning!

You are starting the virtual machine as a visitor to current project. As a visitor, you can change files in the booted virtual machine, but the changed files will be aborted when the server is shut down.