how to generate solver ?

Numerical methods and mathematical models of Elmer
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julilo
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how to generate solver ?

Post by julilo »

cordial greeting community
I am currently working on the development and simulation of a semiconductor diode, and I am not aware of how to generate the equations that properly govern the physical behavior of the semiconductor diode.
My question is how to generate this equation from the beginning, from mathematical operators available in Elmer. This equation is described mathematically as follows:

– ∇ ⋅ ( ε ∇ ψ ) = q ( p – n + N )
– ∇ ⋅ J n = – qRSRH
– ∇ ⋅ J p = qRSRH

These equations contain the following variables:
• ψ indicates electrostatic potential
• q equals the elementary charge
• p and n are the hole and electron concentrations, respectively
• N represents the fixed charge associated with ionized donors
You can express the electron and hole current densities, J n and J p , in terms of ψ, n
and p:

J n = – qnμ n ∇ ψ + qD n ∇ n
J p = – qpμ p ∇ ψ – qD p ∇ p

where μ n and μ p are the carrier mobilities, and D n and D p are the carrier diffusivities.

I would greatly appreciate your contributions !
mzenker
Posts: 1999
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: how to generate solver ?

Post by mzenker »

Hi,

you can find information on solver creation in Elmer in the Solver Manual and in the Programmer's Tutorial.

HTH,
Matthias
raback
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Re: how to generate solver ?

Post by raback »

Hi julilo

This is still relevant:
viewtopic.php?f=15&t=2990&p=17853&hilit=ModelPDE#p9292

Do you have any idea whether your system can be solved weakly coupled or as a monolithic system?

-Peter
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