Title

Book: Guaranteed computation methods for eigenvalue problems of differential operators

Author

xfliu

Description

The codes for numerical examples in the book: Guaranteed computation methods for eigenvalue problems of differential operators.

Properties

Public

  • README
  • 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.
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.

About the directory

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.

(Please login first to start the virtual machine.)

About Machine Type

The machine with type as "n1-standard-1" has 1 CPU Core and 4GB memory. The Google app compute engine provides a detailed guide of the machine type. For more detailed information, please refer to More detail.
If you need a high-spec machine type, please contact the site manager.