pdf 260K - Madagascar

8
PROGRAMMING PART (EXTRA CREDIT)
For extra credit, you can modify the wave modeling program to include anisotropic
wave propagation effects. The program below (slightly modified from the original
version by Paul Sava) implements wave modeling with equation
∂ 2 P
∂t 2
= V 2 (x) ∇ 2 P + F (x, t) = V 2 (x)
( ∂ 2 P
∂x 2 1
+ ∂2 P
∂x 2 2
)
+ F (x, t) , (15)
where F (x, t) is the source term. The implementation uses finite-difference discretization
(second-order in time and fourth-order in space). Stepping in time involves the
following computations:
P t+∆t = [ V 2 (x) ∇ 2 P t + F (x, t) ] ∆t 2 + 2P t − P t−∆t , (16)
where P represents the propagating wavefield discretized at different time steps.
1 /∗ 2−D f i n i t e −d i f f e r e n c e a c o u s t i c wave propagation ∗/
2 #include
3
4 #i f d e f OPENMP
5 #include
6 #endif
7
10
8 static int n1 , n2 ;
9 static float c0 , c11 , c21 , c12 , c22 ;
11 static void l a p l a c i a n ( float ∗∗ uin /∗ [ n2 ] [ n1 ] ∗/ ,
12 float ∗∗ uout /∗ [ n2 ] [ n1 ] ∗/ )
13 /∗ Laplacian operator , 4 th−order f i n i t e −d i f f e r e n c e ∗/
14 {
15 int i1 , i 2 ;
16
17 #i f d e f OPENMP
18 #pragma omp p a r a l l e l for \
19 p r i v a t e ( i2 , i 1 ) \
20 shared ( n2 , n1 , uout , uin , c11 , c12 , c21 , c22 , c0 )
21 #endif
22 for ( i 2 =2; i 2 < n2 −2; i 2++) {
23 for ( i 1 =2; i 1 < n1 −2; i 1++) {
24 uout [ i 2 ] [ i 1 ] =
25 c11 ∗( uin [ i 2 ] [ i1 −1]+uin [ i 2 ] [ i 1 +1]) +
26 c12 ∗( uin [ i 2 ] [ i1 −2]+uin [ i 2 ] [ i 1 +2]) +
27 c21 ∗( uin [ i2 −1][ i 1 ]+ uin [ i 2 +1][ i 1 ] ) +
28 c22 ∗( uin [ i2 −2][ i 1 ]+ uin [ i 2 +2][ i 1 ] ) +
29 c0 ∗ uin [ i 2 ] [ i 1 ] ;
30 }