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Modify basis function evaluation into a single function. Rename files and functions (residualsScript and meshScript).
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‎src/mesh/FEAResidualsScript.js‎

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This file was deleted.

src/mesh/FEAMeshScript.js renamed to src/mesh/meshScript.js

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// |_| | |_ //
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// Website: https://feascript.com/ \__| //
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export class FEAMesh {
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export class meshScript {
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/**
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* Constructor to initialize the Mesh object
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* Constructor to initialize the meshScript class
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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

‎src/mesh/residualsScript.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 residualsScript {
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/**
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* Constructor to initialize the residualsScript class
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* @param {string} dimension - The dimension of the element ('1D' or '2D')
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* @param {number} order - The order of the element
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*/
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constructor({ dimension, order }) {
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this.dimension = dimension;
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this.order = order;
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}
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/**
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* Return the basis functions and their derivatives based on the dimension and order
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* @param {number} ksi - Natural coordinate (for both 1D and 2D)
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* @param {number} [eta] - Second natural coordinate (only for 2D elements)
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* @returns {object} An object containing:
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* - basisFunction: Array of evaluated basis functions
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* - basisFunctionDerivKsi: Array of derivatives of basis functions with respect to ksi
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* - basisFunctionDerivEta: Array of derivatives of basis functions with respect to eta (only for 2D elements)
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*/
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getBasisFunctions(ksi, eta = null) {
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let basisFunction = [];
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let basisFunctionDerivKsi = [];
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let basisFunctionDerivEta = [];
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if (this.dimension === "1D" && this.order === 1) {
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// Linear basis functions for 1D elements
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basisFunction[0] = 1 - ksi;
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basisFunction[1] = ksi;
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// Derivatives of basis functions with respect to ksi
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basisFunctionDerivKsi[0] = -1;
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basisFunctionDerivKsi[1] = 1;
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} else if (this.dimension === "2D" && this.order === 1) {
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if (eta === null) {
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console.log("Eta coordinate is required for 2D elements");
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return;
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}
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// Linear basis functions for 2D elements
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function l1(c) {
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return 1 - c;
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}
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function l2(c) {
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return c;
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}
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function dl1() {
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return -1;
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}
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function dl2() {
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return 1;
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}
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// Evaluate basis functions at (ksi, eta)
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basisFunction[0] = l1(ksi) * l1(eta);
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basisFunction[1] = l1(ksi) * l2(eta);
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basisFunction[2] = l2(ksi) * l1(eta);
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basisFunction[3] = l2(ksi) * l2(eta);
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// Derivatives with respect to ksi
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basisFunctionDerivKsi[0] = dl1() * l1(eta);
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basisFunctionDerivKsi[1] = dl1() * l2(eta);
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basisFunctionDerivKsi[2] = dl2() * l1(eta);
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basisFunctionDerivKsi[3] = dl2() * l2(eta);
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// Derivatives with respect to eta
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basisFunctionDerivEta[0] = l1(ksi) * dl1();
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basisFunctionDerivEta[1] = l1(ksi) * dl2();
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basisFunctionDerivEta[2] = l2(ksi) * dl1();
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basisFunctionDerivEta[3] = l2(ksi) * dl2();
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} else if (this.dimension === "2D" && this.order === 2) {
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if (eta === null) {
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console.log("Eta coordinate is required for 2D elements");
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return;
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}
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// Quadratic basis functions for 2D elements
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function l1(c) {
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return 2 * c ** 2 - 3 * c + 1;
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}
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function l2(c) {
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return -4 * c ** 2 + 4 * c;
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}
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function l3(c) {
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return 2 * c ** 2 - c;
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}
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function dl1(c) {
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return 4 * c - 3;
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}
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function dl2(c) {
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return -8 * c + 4;
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}
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function dl3(c) {
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return 4 * c - 1;
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}
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// Evaluate basis functions at (ksi, eta)
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basisFunction[0] = l1(ksi) * l1(eta);
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basisFunction[1] = l1(ksi) * l2(eta);
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basisFunction[2] = l1(ksi) * l3(eta);
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basisFunction[3] = l2(ksi) * l1(eta);
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basisFunction[4] = l2(ksi) * l2(eta);
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basisFunction[5] = l2(ksi) * l3(eta);
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basisFunction[6] = l3(ksi) * l1(eta);
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basisFunction[7] = l3(ksi) * l2(eta);
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basisFunction[8] = l3(ksi) * l3(eta);
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// Derivatives with respect to ksi
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basisFunctionDerivKsi[0] = dl1(ksi) * l1(eta);
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basisFunctionDerivKsi[1] = dl1(ksi) * l2(eta);
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basisFunctionDerivKsi[2] = dl1(ksi) * l3(eta);
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basisFunctionDerivKsi[3] = dl2(ksi) * l1(eta);
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basisFunctionDerivKsi[4] = dl2(ksi) * l2(eta);
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basisFunctionDerivKsi[5] = dl2(ksi) * l3(eta);
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basisFunctionDerivKsi[6] = dl3(ksi) * l1(eta);
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basisFunctionDerivKsi[7] = dl3(ksi) * l2(eta);
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basisFunctionDerivKsi[8] = dl3(ksi) * l3(eta);
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// Derivatives with respect to eta
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basisFunctionDerivEta[0] = l1(ksi) * dl1(eta);
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basisFunctionDerivEta[1] = l1(ksi) * dl2(eta);
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basisFunctionDerivEta[2] = l1(ksi) * dl3(eta);
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basisFunctionDerivEta[3] = l2(ksi) * dl1(eta);
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basisFunctionDerivEta[4] = l2(ksi) * dl2(eta);
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basisFunctionDerivEta[5] = l2(ksi) * dl3(eta);
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basisFunctionDerivEta[6] = l3(ksi) * dl1(eta);
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basisFunctionDerivEta[7] = l3(ksi) * dl2(eta);
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basisFunctionDerivEta[8] = l3(ksi) * dl3(eta);
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} else {
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console.log("Unsupported dimension or element order");
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}
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return { basisFunction, basisFunctionDerivKsi, basisFunctionDerivEta };
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}
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/**
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* Return Gauss points and weights based on element configuration
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* @returns {object} An object containing:
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* - gaussPoints: Array of Gauss points
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* - gaussWeights: Array of Gauss weights
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*/
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getGaussPointsAndWeights() {
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let gaussPoints = []; // Gauss points
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let gaussWeights = []; // Gauss weights
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if (this.dimension === "1D" && this.order === 1) {
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console.log("Unsupported dimension or element order");
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} else if (this.dimension === "2D" && this.order === 2) {
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// For 2D quadratic elements, use 3-point Gauss quadrature in each direction
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gaussPoints[0] = (1 - Math.sqrt(3 / 5)) / 2;
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gaussPoints[1] = 0.5;
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gaussPoints[2] = (1 + Math.sqrt(3 / 5)) / 2;
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gaussWeights[0] = 5 / 18;
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gaussWeights[1] = 8 / 18;
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gaussWeights[2] = 5 / 18;
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} else {
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console.log("Unsupported dimension or element order");
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}
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return { gaussPoints, gaussWeights };
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}
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}

‎src/solvers/solidHeatScript.js‎

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@@ -8,8 +8,8 @@
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// |_| | |_ //
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// Website: https://feascript.com/ \__| //
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import { FEAElementFunctions } from "../mesh/FEAResidualsScript.js";
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import { FEAMesh } from "../mesh/FEAMeshScript.js";
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import { residualsScript } from "../mesh/residualsScript.js";
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import { meshScript } from "../mesh/meshScript.js";
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/**
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* Generate the matrix and the residual vector for the Finite Element Method in two dimensions
@@ -36,7 +36,7 @@ export function assembleSolidHeatMatrix2D(meshConfig, boundaryConditions) {
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} = boundaryConditions;
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// Create a new instance of the Mesh class for 2D mesh generation
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const mesh2D = new FEAMesh({
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const mesh2D = new meshScript({
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numElementsX,
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numElementsY,
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maxX,
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}
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}
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// Initialize the FEAElementFunctions class
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const elementFunctions = new FEAElementFunctions({
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// Initialize the residualsScript class
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const elementFunctions = new residualsScript({
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dimension: "2D",
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order: 2,
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});

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