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ilogin

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04-25-2011
02:41 AM

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Helmholtz 2d boundary conditions

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

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Alexander_K_Intel2

Employee

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04-25-2011
03:00 AM

51 Views

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

mecej4

Black Belt

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04-25-2011
04:10 AM

51 Views

The resolution is simple. Simply specify the value at one point, say, (a

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

ilogin

Beginner

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04-25-2011
04:48 AM

51 Views

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

mecej4

Black Belt

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04-25-2011
05:36 AM

51 Views

And, when you wrote in your first post that

did you refer to

In the problem that you want to solve, is

ilogin

Beginner

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04-25-2011
06:02 AM

51 Views

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.

Alexander_K_Intel2

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04-25-2011
10:11 AM

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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

ilogin

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04-26-2011
12:28 AM

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Thank you,

Ilya

Alexander_K_Intel2

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05-03-2011
04:37 AM

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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

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