DAB_HE

A Julia implementation of the Double Absorbing Boundary (DAB) method applied in a high-order spectral element method for solving the Helmholtz equation in 2D. This implementation follows the methodology presented in [1]. The current version of the code relates to the setup presented in Section 6.1 of the paper. This code was developed during my time as a postdoctoral fellow in the Faculty of Aerospace Engineering at the Technion - Israel Institute of Technolgoy.

[1] S. Papadimitropoulos, D. Givoli, The Double Absorbing Boundary method for the Helmholtz equation, Applied Numerical Mathematics (2021).

Overview

This project implements a numerical solver for the Helmholtz equation using a high-order spectral element method with the Double Absorbing Boundary method. The implementation is written in Julia and provides efficient numerical methods for solving wave propagation problems.

Project Structure

The project consists of several Julia modules:

• DAB_HE.jl: Main solver implementation
• Mesh2Drect.jl: 2D rectangular mesh generation
• basis.jl and basisx.jl: Basis functions implementation
• intNodes.jl and intWeights.jl: Integration nodes and weights
• femerror.jl: Error computation
• Various integration modules (I1.jl through I6.jl, ID.jl)
• Supporting utilities for sorting, node checking, and function evaluation

Dependencies

• Julia programming language
• SparseArrays
• LinearAlgebra

Usage

1. Ensure you have Julia installed on your system
2. Install the required dependencies:

   using Pkg
   Pkg.add(["SparseArrays", "LinearAlgebra"])

3. Clone this repository
4. Run the main solver:

   include("DAB_HE.jl")