topic Helmholtz 2d boundary conditions in Intel® oneAPI Math Kernel Library

Helmholtz 2d boundary conditions

ilogin — Mon, 25 Apr 2011 09:41:06 GMT

Dears,

I need your help with the subj. The problem is that my function is not defined on boundaries. Description of d_commit_Helmholtz_2D shows that it finds solution inside target area (ax

This is confusing for me because i do not know function values on the boundaries. I need to solve 2D Helmholtz problem with 0 Neiman conditions and i do not know what to write on boundaries into F because of special sort of my equation. I cannot find the values on boundaries.

Thank you in advance for your help.

Regards,

Ilya

Helmholtz 2d boundary conditions

Alexander_K_Intel2 — Mon, 25 Apr 2011 10:00:55 GMT

Hi Ilya,

Could you describe you problem in details? It is not clear for me why you don't know values of rhs.If you want you could answer me in private mode.

With best regards,

Alexander Kalinkin

Helmholtz 2d boundary conditions

mecej4 — Mon, 25 Apr 2011 11:10:05 GMT

If all the boundary conditions are Neumann b.c., the solution is indeterminate by a constant. In other words, if u(x,y) is a solution, so is u + C. There will be a corresponding indeterminancy in the discretized problem, as well.

The resolution is simple. Simply specify the value at one point, say, (a_x, a_y) to be any value that you like, such as zero.

Another artifice is to use v = u/x ( or, if better suited, u/y) as the dependent variable.

Helmholtz 2d boundary conditions

ilogin — Mon, 25 Apr 2011 11:48:08 GMT

Hello,

Let me clarify. My problem looks likeu/x+u/y=-F(x,y). Boundary conditions areu/x=0|(x=0,x=Lx) andu/y=0|(y=0,y=Ly). F is not defined on boundaries because of problem statement. So currently I cannot see the way to implement your idea.

MKL function force me to pass boundary values into array F but values are not defined.

Thank you,

Ilya

Helmholtz 2d boundary conditions

mecej4 — Mon, 25 Apr 2011 12:36:22 GMT

> My problem looks likeu/x+u/y=-F(x,y)

That is the Poisson equation, not the Helmholtz equation -- the latter has the additional term q . u in it, where q is a constant. Please clarify which equation you want to solve.

And, when you wrote in your first post that

> The problem is that my function is not defined on boundaries

did you refer to u or to F as "my function" ?

In the problem that you want to solve, is F known as an analytical expression? If not, how is it known?

Helmholtz 2d boundary conditions

ilogin — Mon, 25 Apr 2011 13:02:17 GMT

I'm sorry for the inconvenience. The issue is with F.

F is defined as an array of values in the area 0<1, 0<1. Therefore I don't know values for F on the boundaries. I do not have any analytical expression for F since I compute it in sophisticated iteration process.

I use d_Helmholtz_2D function to compute my problem. As far as I know there is no separate function for poisson problem so I use q=0.

Helmholtz 2d boundary conditions

Alexander_K_Intel2 — Mon, 25 Apr 2011 17:11:45 GMT

Gents,

It's seems we have some misunderstanding. For differential problem one doesnt know values of rhs on boundary of domain. But for algebraic problem that comes from differential one need to set value on boundary (for example continue rhs from domain to its boundary).

With best regards,

Alexander Kalinkin

Helmholtz 2d boundary conditions

ilogin — Tue, 26 Apr 2011 07:28:24 GMT

Thank you guys! I need to find a way how to extend F values for boundaries and not to break physical meaning of problem. This is not good that MKL function requires values for its arguments stronger than stated in documentation.

Thank you,

Ilya

Helmholtz 2d boundary conditions

Alexander_K_Intel2 — Tue, 03 May 2011 11:37:04 GMT

Ilia,

MKL uses a standard 5-point approximation of 2D Helmholtz problem. But Poisson library from MKL requires values of rhs on Neumann boundary to find values of solution on this boundary. So, if you want to use Helmholtz functionality you need to implement next trick:

If want to solve Helmholtz equation in domain (a_x, b_x)*(a_y, b_y) with nx and ny mesh intervals correspondently then call Poisson library with parameters as follows:

ax_new = a_x+(bx-ax)/nx;

bx_new = b_x-(bx-ax)/nx;

ay_new = a_y+(by-ay)/ny;

by_new = b_y-(by-ay)/ny;

nx_new = nx-2;

ny_new = ny-2;

d_init_Helmholtz_2D(&ax_new, &bx_new, &ay_new, &by_new, &nx_new, &ny_new, BCtype, &q, ipar, dpar, &stat);

d_commit_Helmholtz_2D(f, bd_ax, bd_bx, bd_ay, bd_by, &xhandle, ipar, dpar, &stat);

ets

With best regards,

Alexander Kalinkin