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‎CONTRIBUTING.md‎

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## Contributing to FEAScript
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Thank you for your interest in contributing!</br>
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FEAScript is in early development with continuous addition of new features and improvements. To ensure a smooth and collaborative development process, please review and follow the guidelines.
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## Contribution Guidelines
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1. Search the <a href="https://github.com/FEAScript/FEAScript/wiki/Roadmap" target="_blank">project roadmap</a> to see areas where help is needed.
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2. Respect the existing FEAScript coding style. Observe the code near your intended change and attempt to preserve that style with your modifications.
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3. We recommend using <a href="https://code.visualstudio.com/" target="_blank">Visual Studio Code</a> with the <a href="https://marketplace.visualstudio.com/items?itemName=esbenp.prettier-vscode" target="_blank">Prettier</a> plugin for automatic code formatting.
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4. Ensure that you use <a href="https://en.wikipedia.org/wiki/Camel_case" target="_blank">camelCase</a> formatting for variable names throughout the code.
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5. Before committing, you can test your modifications by running the FEAScript library from a local server. To do this, use a <a href="https://docs.python.org/3/library/http.server.html" target="_blank">Python HTTP Server</a> by executing the following <a href="https://github.com/FEAScript/FEAScript-website/blob/main/corsHttpServer.py" target="_blank">script</a>. Start the Python server by running `python3 corsHttpServer.py` in your local repository folder. The server address will be http://127.0.0.1:8000/. For more details, see the instructions under the 'Import the FEAScript library from a local server' section in the <a href="https://github.com/FEAScript/FEAScript-website/blob/main/exampleHeatTrasnfer.html" target="_blank">2D heat transfer example</a>.

‎LICENSE‎

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MIT License
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Copyright (c) 2024 FEAScript
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.

‎README.md‎

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<img src="https://feascript.github.io/FEAScript-website/images/FEAScriptLogo.png" width="80" >
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## Introduction
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<a href="https://feascript.com/" target="_blank">FEAScript</a> is an open-source JavaScript library for solving differential equations using the finite element method. It allows you to create and run browser-based simulations of physics and engineering problems.
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<br>
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</br>
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FEAScript is in early-development and new features and improvements are constantly being added.
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<!-- <img src="https://feascript.github.io/FEAScript-website/images/example1.png" width="400" > -->
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## Contributing
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We are actively seeking developers to help evolve FEAScript. Please refer to <a href="./CONTRIBUTING.md" target="_blank">CONTRIBUTING.md</a> for instructions on how to contribute.
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## License
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FEAScript is distributed under the terms of the <a href="./LICENSE" target="_blank">MIT license</a>. &#169; 2024 FEAScript.

‎src/FEAScript.js‎

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// ______ ______ _____ _ _ //
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// | ____| ____| /\ / ____| (_) | | //
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// | |__ | |__ / \ | (___ ___ ____ _ ____ | |_ //
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// | __| | __| / /\ \ \___ \ / __| __| | _ \| __| //
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// | | | |____ / ____ \ ____) | (__| | | | |_) | | //
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// |_| |______/_/ \_\_____/ \___|_| |_| __/| | //
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// | | | | //
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// |_| | |_ //
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// Website: https://feascript.com/ \__| //
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import { assembleSolidHeatMatrix2D } from "./solvers/solidHeatScript.js";
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/**
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* Differential equations solver using the finite element method
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* @param {string} solverScript - Parameter specifying the type of solver
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* @param {object} meshConfig - Object containing computational mesh details
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* @param {object} boundaryConditions - Object containing boundary conditions for the finite element analysis
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* @returns {object} An object containing the solution vector and additional mesh information
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*/
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export function FEAScript(solverScript, meshConfig, boundaryConditions) {
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let jacobianMatrix = []; // Jacobian matrix
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let residualVector = []; // Galerkin residuals
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let totalNodesX; // Total number of nodes along x-axis
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let totalNodesY; // Total number of nodes along y-axis
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let nodeXCoordinates = []; // Array to store x-coordinates of nodes (local numbering)
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let nodeYCoordinates = []; // Array to store y-coordinates of nodes (local numbering)
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let solutionVector = []; // Solution vector
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// Assembly matrices
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console.time("assemblyMatrices");
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if (solverScript === "solidHeatScript") {
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console.log("solverScript:", solverScript);
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({
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jacobianMatrix,
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residualVector,
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totalNodesX,
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totalNodesY,
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nodeXCoordinates,
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nodeYCoordinates,
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} = assembleSolidHeatMatrix2D(meshConfig, boundaryConditions));
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}
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console.timeEnd("assemblyMatrices");
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let numNodesX = totalNodesX; // Assign the value of totalNodesX to numNodesX
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let numNodesY = totalNodesY; // Assign the value of totalNodesY to numNodesY
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// System solving
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console.time("systemSolving");
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solutionVector = math.lusolve(jacobianMatrix, residualVector); // Solve the system of linear equations using LU decomposition
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console.timeEnd("systemSolving");
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// Debugger;
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//console.log(x); // Log the solution to the console
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// Return the solution matrix
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return {
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solutionVector,
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numNodesX,
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numNodesY,
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nodeXCoordinates,
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nodeYCoordinates,
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};
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}

‎src/index.js‎

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// ______ ______ _____ _ _ //
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// | ____| ____| /\ / ____| (_) | | //
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// | |__ | |__ / \ | (___ ___ ____ _ ____ | |_ //
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// | __| | __| / /\ \ \___ \ / __| __| | _ \| __| //
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// | | | |____ / ____ \ ____) | (__| | | | |_) | | //
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// |_| |______/_/ \_\_____/ \___|_| |_| __/| | //
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// | | | | //
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// |_| | |_ //
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// Website: https://feascript.com/ \__| //
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export { FEAScript } from "./FEAScript.js";
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export { plotSolution2D } from "./visualization/plotSolutionScript.js";
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export { FEAScriptVersion } from "./utilities/helperFunctionsScript.js";

‎src/mesh/FEAMeshScript.js‎

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// ______ ______ _____ _ _ //
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// | ____| ____| /\ / ____| (_) | | //
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// | |__ | |__ / \ | (___ ___ ____ _ ____ | |_ //
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// | __| | __| / /\ \ \___ \ / __| __| | _ \| __| //
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// | | | |____ / ____ \ ____) | (__| | | | |_) | | //
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// |_| |______/_/ \_\_____/ \___|_| |_| __/| | //
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// | | | | //
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// |_| | |_ //
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// Website: https://feascript.com/ \__| //
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export class FEAMesh {
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/**
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* Constructor to initialize the Mesh object
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* @param {object} config - Configuration object for the mesh
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* @param {number} config.numElementsX - Number of elements along the x-axis
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* @param {number} config.maxX - Maximum x-coordinate of the mesh
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* @param {number} [config.numElementsY=1] - Number of elements along the y-axis (default is 1 for 1D meshes)
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* @param {number} [config.maxY=0] - Maximum y-coordinate of the mesh (default is 0 for 1D meshes)
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* @param {string} [config.dimension='2D'] - The dimension of the mesh, either 1D or 2D (default is 2D)
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* @param {string} [config.meshFile=null] - Optional mesh file (JSON) for predefined meshes
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*/
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constructor({
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numElementsX,
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maxX,
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numElementsY = 1,
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maxY = 0,
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dimension = "2D",
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meshFile = null,
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}) {
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this.numElementsX = numElementsX;
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this.numElementsY = numElementsY;
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this.maxX = maxX;
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this.maxY = maxY;
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this.dimension = dimension;
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this.meshFile = meshFile;
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}
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/**
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* Generate the mesh based on the dimension or custom mesh file
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* @returns {object} The generated mesh containing node coordinates and total nodes
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*/
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generateMesh() {
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if (this.meshFile) {
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// If a custom mesh file is provided, read and parse it
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const meshData = this.generateMeshFromCustomFile(this.meshFile);
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return meshData;
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} else {
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// Generate mesh based on dimension
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if (this.dimension === "1D") {
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return this.generateMesh1D();
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} else {
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return this.generateMesh2D();
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}
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}
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}
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/**
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* Parse a custom mesh JSON file and generate the mesh
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* @param {string} meshFilePath - Path to the custom mesh file (JSON format)
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* @returns {object} Mesh data containing coordinates and connectivity
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*/
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generateMeshFromCustomFile(meshFilePath) {
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const response = fetch(meshFilePath);
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const meshData = response.json();
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const nodeXCoordinates = [];
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const nodeYCoordinates = [];
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const { nodes, elements } = meshData;
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// Parse the node coordinates
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nodes.forEach((node) => {
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nodeXCoordinates.push(node.x);
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nodeYCoordinates.push(node.y);
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});
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return {
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nodeXCoordinates,
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nodeYCoordinates,
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totalNodesX: nodeXCoordinates.length,
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totalNodesY: nodeYCoordinates.length,
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elements,
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};
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}
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/**
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* Generate a one-dimensional mesh along the x-axis
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* The method divides the x-axis into equal segments based on the number of elements
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* @returns {object} An object containing the x-coordinates of the nodes and the total number of nodes along the x-axis
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*/
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generateMesh1D() {
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let nodeXCoordinates = [];
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const xStart = 0;
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let totalNodesX = 2 * this.numElementsX + 1;
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const deltaX = (this.maxX - xStart) / this.numElementsX;
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nodeXCoordinates[0] = xStart;
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for (let i = 1; i < totalNodesX; i++) {
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nodeXCoordinates[i] = nodeXCoordinates[i - 1] + deltaX;
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}
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return { nodeXCoordinates, totalNodesX };
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}
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/**
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* Generate a two-dimensional structured mesh.
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* The method creates a structured grid where nodes are placed at regular intervals along the x and y axes
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* @returns {object} An object containing the x and y coordinates and the total number of nodes
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*/
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generateMesh2D() {
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let nodeXCoordinates = [];
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let nodeYCoordinates = [];
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const xStart = 0;
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const yStart = 0;
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let totalNodesX = 2 * this.numElementsX + 1;
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let totalNodesY = 2 * this.numElementsY + 1;
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const deltaX = (this.maxX - xStart) / this.numElementsX;
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const deltaY = (this.maxY - yStart) / this.numElementsY;
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nodeXCoordinates[0] = xStart;
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nodeYCoordinates[0] = yStart;
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for (let i = 1; i < totalNodesY; i++) {
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nodeXCoordinates[i] = nodeXCoordinates[0];
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nodeYCoordinates[i] = nodeYCoordinates[0] + (i * deltaY) / 2;
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}
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for (let i = 1; i < totalNodesX; i++) {
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const nnode = i * totalNodesY;
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nodeXCoordinates[nnode] = nodeXCoordinates[0] + (i * deltaX) / 2;
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nodeYCoordinates[nnode] = nodeYCoordinates[0];
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for (let j = 1; j < totalNodesY; j++) {
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nodeXCoordinates[nnode + j] = nodeXCoordinates[nnode];
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nodeYCoordinates[nnode + j] =
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nodeYCoordinates[nnode] + (j * deltaY) / 2;
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}
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}
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// Generate nodal numbering (NOP) array
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const nodalNumbering = this.generateNodalNumbering(
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this.numElementsX,
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this.numElementsY,
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totalNodesX,
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totalNodesY
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);
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// Return x and y coordinates of nodes, total nodes, and NOP array
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return {
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nodeXCoordinates,
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nodeYCoordinates,
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totalNodesX,
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totalNodesY,
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nodalNumbering,
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};
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}
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/**
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* Generate the nodal numbering (NOP) array for a 2D structured mesh
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* This array represents the connectivity between elements and their corresponding nodes
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* @param {number} numElementsX - Number of elements along the x-axis
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* @param {number} numElementsY - Number of elements along the y-axis
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* @param {number} totalNodesX - Total number of nodes along the x-axis
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* @param {number} totalNodesY - Total number of nodes along the y-axis
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* @returns {array} NOP - A 2D array which represents the element-to-node connectivity for the entire mesh
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*/
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generateNodalNumbering(numElementsX, numElementsY, totalNodesX, totalNodesY) {
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let elementIndex = 0;
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let nop = [];
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for (let i = 0; i < numElementsX * numElementsY; i++) {
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nop.push([]);
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for (let j = 0; j < 9; j++) {
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nop[i][j] = 0;
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}
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}
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/*
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Representation of the nodes in the case of quadratic rectangular elements
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2__5__8
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| |
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1 4 7
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|__ __|
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0 3 6
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*/
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for (let i = 1; i <= numElementsX; i++) {
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for (let j = 1; j <= numElementsY; j++) {
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for (let k = 1; k <= 3; k++) {
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let l = 3 * k - 2;
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nop[elementIndex][l - 1] = totalNodesY * (2 * i + k - 3) + 2 * j - 1;
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nop[elementIndex][l] = nop[elementIndex][l - 1] + 1;
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nop[elementIndex][l + 1] = nop[elementIndex][l - 1] + 2;
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}
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elementIndex = elementIndex + 1;
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}
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}
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return nop;
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}
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}

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