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nkliuyueming April 29, 2011 16:23

I developed an FEM toolkit in Java: FuturEye
FuturEye is a Java based Finite Element Method (FEM) Toolkit, providing concise, natural and easy understanding programming interfaces for users who wish to develop researching and/or engineering FEM algorithms for Forward and/or Inverse Problems.

The essential components of FEM are abstracted out, such as nodes, elements, meshes, degrees of freedom and shape function etc. The data and operations of these classes are encapsulated together properly. The classes that different from other existing object-oriented FEM softwares or libraries are function classes. The behavior of the function classes in Futureye is very similar to that in mathematical context. For example algebra of functions, function derivatives and composition of functions. Especially in FEM environment, shape functions, Jacobin of coordinate transforms and numerical integration are all based on the function classes. This feature leads to a more close integration between theory and computer implementation.

FuturEye is designed to solve 1D,2D and 3D partial differential equations(PDE) of scalar and/or vector valued unknown functions. The start point of development of this toolkit is solving inverse problems of PDE. In order to solve inverse problems, usually some forward problems must be solved first and many exterior data manipulations should be performed during the solving processes. There are many classes defined for those data operations. However, the data processes are complicated in actual applications, we can not write down all the tools for manipulating data. The design of the basic classes allows operations to all aspect of data structure directly or indirectly in an easily understanding way. This is important for users who need write their own operations or algorithms on the bases of data structure in FuturEye. Some other existing FEM softwares or libraries may over encapsulate the data and operations for such inverse applications.

The toolkit can be used for various purposes:
  • Teaching: The feature of close integration between FEM theory and computer implementation of this toolkit helps a student to understand basic FEM concepts, e.g. shape functions, Jacobin and assembly process.
  • Researching: Helps researchers quickly develop and test their models, experiment data and algorithms. e.g. new equations, new finite elements and new solution methods.
  • Engineering: The performance and efficiency may be unsatisfied for real applications, if an finite element class defined in a mathematical manner without optimization. Thanks to the interface conception in Java, we can implement the same interface in many different ways, thus a carefully optimized finite element class can be used in applications with huge number of elements.

nkliuyueming October 25, 2011 22:47

update to version 2.1
How to use WeakFormBuilder:

package edu.uta.futureye.tutorial;

import java.util.HashMap;

import edu.uta.futureye.algebra.SolverJBLAS;
import edu.uta.futureye.algebra.intf.Matrix;
import edu.uta.futureye.algebra.intf.Vector;
import edu.uta.futureye.core.Element;
import edu.uta.futureye.core.Mesh;
import edu.uta.futureye.core.NodeType;
import edu.uta.futureye.function.AbstractFunction;
import edu.uta.futureye.function.Variable;
import edu.uta.futureye.function.basic.FC;
import edu.uta.futureye.function.basic.FX;
import edu.uta.futureye.function.intf.Function;
import edu.uta.futureye.function.intf.ScalarShapeFunction;
import edu.uta.futureye.lib.assembler.AssemblerScalar;
import edu.uta.futureye.lib.element.FEBilinearRectangle;
import edu.uta.futureye.lib.element.FEBilinearRectangleRegular;
import edu.uta.futureye.lib.element.FELinearTriangle;
import edu.uta.futureye.lib.weakform.WeakFormBuilder;
import edu.uta.futureye.util.container.ElementList;

public class UseWeakFormBuilder {

* <blockquote><pre>
* Solve
* -k*\Delta{u} = f in \Omega
* u(x,y) = 0, on boundary x=3.0 of \Omega
* u_n + u = 0.01, on other boundary of \Omega
* where
* \Omega = [-3,3]*[-3,3]
* k = 2
* f = -4*(x^2+y^2)+72
* u_n = \frac{\partial{u}}{\partial{n}}
* n: outer unit normal of \Omega
* </blockquote></pre>
public static void rectangleTest() {
//1.Read in a rectangle mesh from an input file with
// format ASCII UCD generated by Gridgen
MeshReader reader = new MeshReader("rectangle.grd");
Mesh mesh = reader.read2DMesh();

//2.Mark border types
HashMap<NodeType, Function> mapNTF = new HashMap<NodeType, Function>();
//Robin type on boundary x=3.0 of \Omega
mapNTF.put(NodeType.Robin, new AbstractFunction("x","y"){
public double value(Variable v) {
if(3.0-v.get("x") < 0.01)
return 1.0; //this is Robin condition
return -1.0;
//Dirichlet type on other boundary of \Omega
mapNTF.put(NodeType.Dirichlet, null);

//3.Use element library to assign degrees of
// freedom (DOF) to element
ElementList eList = mesh.getElementList();
//FEBilinearRectangle bilinearRectangle = new FEBilinearRectangle();
//If the boundary of element parallel with coordinate use this one instead.
//It will be faster than the old one.
FEBilinearRectangleRegular bilinearRectangle = new FEBilinearRectangleRegular();
for(int i=1;i<=eList.size();i++)

//4.Weak form. We use WeakFormBuilder to define weak form
WeakFormBuilder wfb = new WeakFormBuilder() {
* Override this function to define weak form
public Function makeExpression(Element e, Type type) {
ScalarShapeFunction u = getScalarTrial();
ScalarShapeFunction v = getScalarTest();
//Call param() to get parameters, do NOT define functions here
//except for constant functions (or class FC). Because functions
//will be transformed to local coordinate system by param()
Function fk = param(e,"k");
Function ff = param(e,"f");
switch(type) {
case LHS_Domain:
// k*(u_x*v_x + u_y*v_y) in \Omega
return fk.M( u._d("x").M(v._d("x")) .A (u._d("y").M(v._d("y"))) );
case LHS_Border:
// k*u*v on Robin boundary
return fk.M(u.M(v));
case RHS_Domain:
return ff.M(v);
case RHS_Border:
return v.M(0.01);
return null;
Function fx = FX.fx;
Function fy = FX.fy;
wfb.addParamters(FC.c(2.0), "k");
//Right hand side(RHS): f = -4*(x^2+y^2)+72

//5.Assembly process
AssemblerScalar assembler =
new AssemblerScalar(mesh, wfb.getScalarWeakForm());
System.out.println("Begin Assemble...");
Matrix stiff = assembler.getStiffnessMatrix();
Vector load = assembler.getLoadVector();
//Boundary condition
System.out.println("Assemble done!");

//6.Solve linear system
SolverJBLAS solver = new SolverJBLAS();
Vector u = solver.solveDGESV(stiff, load);
for(int i=1;i<=u.getDim();i++)
System.out.println(String.format("%.3f", u.get(i)));

//7.Output results to an Techplot format file
MeshWriter writer = new MeshWriter(mesh);
writer.writeTechplot("./tutorial/UseWeakFormBuilder2.dat", u);

public static void main(String[] args) {


nkliuyueming June 20, 2012 02:25


Scala Language Version: ScalaFEM0.1

cfdnewbie June 20, 2012 02:48


Originally Posted by nkliuyueming (Post 367367)

Scala Language Version: ScalaFEM0.1

just a quick remark: In your plot, it should be Lagrange multiplier, not language multiplier :)

nkliuyueming June 20, 2012 10:02

many thanks!

nkliuyueming July 30, 2012 02:22

Does anyone interested in developing this project?
I have a plan to extend and optimize the toolkit, FuturEye, if you are interested in developing FEM code, please contact me:)

vonboett August 3, 2012 05:26

So it is OpenSource (MIT) right? At ETH Zürich we developed once a Software for simulating soil salinisation (SimSalin) in Java including groundwater flow, evapotranspiration and transport, and we came to the point to see that Java is too slow. Since Java is so close related to C++, would it be worth the effort to rewrite part of your code in C++ and call the methods from Java? The discrete element software FARO for Rockfall protection nets for which I implement new Elements has a Java3D Interface and calls C++ methods and is among the fastest codes of its kind.

nkliuyueming January 29, 2016 14:28

Since google code has been closed I have moved the project to Github:

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