# Numerical Methods Help

1. Mar 20, 2005

### physmurf

Numerical Methods Help!!

I have been trying to understand the differences between Finite-Difference Time-Domain (FDTD), Finite Volume, and the Finite Elements methods of solving Maxwell's equations numerically. I have used the FDTD method for solving Maxwells Equations. I did this without knowing anything about the other two methods. So, now I need to know how FDTD is different from the other two.

Thanks

2. Mar 20, 2005

### clive

In the finite elements approach you compute a solution of the differential equation on each element and then you "assemble" these individual solutions into a global one. So you solve your differential equation on each element.

In the finite difference approach you work always with global solutions. The differential operators are represented by matrices and the differential equation is reduced to a linear system of equations. Solving this system you obtain directly the solution of the differential equation.

Another difference consists of the fact that the finite element method is limited to a well defined class of differential equations (see Lax-Milgram theorem).

Hope it helps
clive

Last edited: Mar 20, 2005
3. Mar 20, 2005

### physmurf

That's a great help clive. You don't happen to know anything about the finite volume approach?

Thanks again

Kurt

4. Mar 21, 2005

### clive

5. Mar 21, 2005

Finite volume methods are used when you have a conservation law to work with. Something like $$u_t + f_x = 0$$ where f(u) is a flux. Rather than just evaluating u at grid points as you do in finite differences, you need to average u over little cells to get the value for a point. You have to make sure what goes out of cell i is going into cell i+1. Finite volume methods can be useful if you're trying to handle a shock without screwing everything up.

6. Mar 22, 2005

### SpaceTiger

Staff Emeritus
What should you use if you do want to screw everything up?

7. Mar 22, 2005

### HallsofIvy

Staff Emeritus
Ah, now I'm an expert on that!

8. Mar 22, 2005