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Dirac Delta function

Soogeun_Kim
Beginner
176 Views
How is the Dirac Delta Function expressed in visual fortran?
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4 Replies
Andrey_Kuzmin__Intel
176 Views
Why do you need it in Fortran? Dirac Delta funtion has no sense inmachine ariphmetic, becausethere is no pointinprecise comparison of floating point numbers and its definition from integration point of view is also meaningless in this case.
Soogeun_Kim
Beginner
176 Views

Thank you for your prompt reply.

I'm solving the 2D Helmholtz problem on a Cartesian plane. u''(x,y)+q*u(x,y)=f(x,y)

Above governing equation, f(x,y) is external or internal source and Dirac Delta Function.

I want to compare analytical solution with numerical solution.

I have analytical solution.

To obtain numerical solution, Dirac Delta Funtion code is needed.

I know the function can not be expressed directly.

So, in detail, my question is how is the approximated expression of Dirac Delta Function.

Thank you in advance

Soogeun Kim

Alexander_K_Intel2
176 Views
Hi,
Am I right that you set delta function as rhs of your Helmholtz equation? And you have solver that provide solution of your problem as smooth function of (x,y)?
With best regards,
Alexander Kalinkin
mecej4
Black Belt
176 Views
A general purpose PDE solver is usually not designed to model singularities. When a discretized version of the PDE is solved, near the singularity the solution will be sensitive to the fineness of the mesh in the neighborhood. Some FEM solvers have special elements (e.g. "crack" elements) that patch a local mathematical solution near the singularity to the smooth, bounded, solution away from the singularity.

Singularities make for beautiful mathematical solutions. They are physically incorrect and numerically intractable. It is quite unreasonable to expect a general purpose language such as Fortran to have special features to treat singularities.
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