The SBP operators are constructed by the Matlab-functions
SBP_I6 6th order Implicit
SBP_I8 8th order Implicit
SBP_I10 10th order Implicit
SBP_I12 12th order Implicit
SBP_SL4 SL order 4
SBP_SL6 SL order 6
You call with the number of grid-points (m) and width of domain (L)
Return parameters are
ST Artificial dissipation (S=S’<=0)
MM = (-M + BD) in second derivative SBP (M=M’>=0)
BD Boundary derivative in second derivative SBP
QQ Q+1/2*B first derivative SBP (Q+Q’=0)
H The norm
xx Grid-points (between 0 and L)
h Grid-step
This is an example of a function call to construct the SL 6 operators
[ST,MM,BD,QQ,H,xx,h] = SBP_SL6(m, L); % Construct SL6 SBP
In the Matlab script “Wave_Implicit_JCP.m” we solve the second order wave equation with Neumann boundary conditions. Here using SBP_SL6
And RK4 for time-integration.
D2 operator = inv(H)*MM
D1 operator = inv(H)*QQ