3D Finite different method using matlab

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Discussion Overview

The discussion centers around solving the 3D diffusion equation using the finite difference method (FDM) in MATLAB. Participants explore the formulation of the problem, including the definition of stencils and matrix setups for numerical implementation.

Discussion Character

  • Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant requests guidance on solving the 3D diffusion equation modeled with FDM in MATLAB.
  • Another participant suggests a specific approach using a stencil that incorporates nearest and next nearest neighbors on a cubic periodic domain, providing definitions for indexing and matrix setup.
  • A similar suggestion is reiterated with a request for further clarification or learning opportunities from the responder.
  • Another participant questions the initial poster's willingness to attempt the problem independently and notes the absence of information regarding the time update algorithm being used.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express differing levels of willingness to engage with the problem independently and provide varying degrees of technical detail.

Contextual Notes

Participants have not clarified specific assumptions regarding the time update algorithm or the overall approach to the finite difference method, which may affect the discussion.

nnadiya
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Can anyone show me how to solve the 3D diffusion equation which has been modeled into FDM by using matlab?
 
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Suppose your stencil only uses nearest and next nearest neighbors on a cubic periodic domain with N lattice points in each direction. Define I am = (1:N)-1;Im(Im==0)=N; and Ip = 2:N+1;Ip(Ip==N+1)=1; Define your system and matrices and use A(lp,lp,lm) ## \sim A_{i+1,i+1,i-1} ## in your stencil.
 
Strum said:
Suppose your stencil only uses nearest and next nearest neighbors on a cubic periodic domain with N lattice points in each direction. Define I am = (1:N)-1;Im(Im==0)=N; and Ip = 2:N+1;Ip(Ip==N+1)=1; Define your system and matrices and use A(lp,lp,lm) ## \sim A_{i+1,i+1,i-1} ## in your stencil.
Can I learn further from you?
 
You are sure you don't want to try yourself first? Also you haven't mentioned which time update algorithm you are using.
 

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