How to generate two PEC boundary conditions in 1D FDTD?

I want to implement a boundary condition in a 1D FDTD for Maxwells Equations in which the field is Purely Reflected in Both the boundaries for the electric field.

In short :

How to generate two PEC walls in 1D FDTD ? What is the boundary condition?

Answer 1

[Shouri Chatterjee]

I am using a template from Prof John B Schneider's book on understanding FDTD, with a minor modification. Increase the size of the E-field array by 1. The end edge of the E-field is now set to 0. Don't recompute this. Compute the H-field all the way to the end, based on this outer E-field.

Reference:

• Understanding the Finite-Difference Time-Domain Method, John B. Schneider, www.eecs.wsu.edu/~schneidj/ufdtd, 2010.

The below code is a modification of Program 3.1. Program 3.1 had a PEC at x=0, a PMC at x=200. The code below has a PEC at x=0, a PEC at x=201.

#include <stdio.h>
#include <math.h>
#define SIZE 200
int main()
{
double ez[SIZE+1] = {0.}, hy[SIZE] = {0.}, imp0=377.0;
int qTime, maxTime = 1000, mm;
char basename[80] = "sim", filename[100];
int frame=0;
FILE* snapshot;

/* do time stepping */
for (qTime = 0; qTime < maxTime; qTime++) {
	/* Magnetic field */
	for(mm=0; mm < SIZE; mm++)
		hy[mm] = hy[mm] + (ez[mm+1]-ez[mm])/imp0;
	/* Electric field */
	for(mm=1; mm < SIZE; mm++)
		ez[mm] = ez[mm] + (hy[mm]-hy[mm-1]) * imp0;
	/* Additive current source at node 50 */
	ez[50] += exp(-(qTime -30.) * (qTime - 30.) / 100.);
//	Explicit forcing function at node 0
//	ez[0] = exp(-(qTime - 30.) * (qTime - 30.) / 100.);
	if (qTime % 10 == 0) {
		sprintf(filename, "%s.%d", basename, frame++);
		snapshot = fopen(filename, "w");
		for(mm=0; mm<SIZE+1; mm++)
			fprintf(snapshot, "%g\n", ez[mm]);
		fclose(snapshot);
	}
}
return 0;
}

[RANIT ROY]

That seems interesting! So we are forcing a secondary source at the Magnetic Field Reflector! Thank You for suggesting this, I shall try this out.