Re: [deal.II] Question about how to get the Stiffness matrix partial derivative with respect to density

2023-08-10 Thread blais...@gmail.com
Dear Lance, It would be easier if you posted the PDE you wish to solve and it's weak form. This would enable us to help you write the Jacobian for it. Currently, it is difficult to fully understand what you are trying to achieve. Best Bruno On Monday, July 24, 2023 at 4:13:21 p.m. UTC-4 dim...@g

Re: [deal.II] Question about how to get the Stiffness matrix partial derivative with respect to density

2023-07-24 Thread Lance Zhang
Hello Wolfgang, thanks for your reply. Currently,I would like to get the sensitivity by using gradient of objective function with respect to density. The Objective function is a vector of movement which is calculated from Ax=b. J=|x|norm1 is the objective function. dJ(x,Θ)/dΘ is the gradient th

Re: [deal.II] Question about how to get the Stiffness matrix partial derivative with respect to density

2023-07-24 Thread Wolfgang Bangerth
On 7/24/23 11:24, Lance Zhang wrote: One moire question,how could I get  ∂A(θ)/∂θx,because I did not find any information about density vector like  θ=[θ1,θ2,...,θm],may I know if I have to set density vector value in this finite element? Lance -- I have no idea. I don't know the program, bu

Re: [deal.II] Question about how to get the Stiffness matrix partial derivative with respect to density

2023-07-24 Thread Lance Zhang
Hello Wolfgang, The value of A^-1(θ))(-∂A(θ)/∂θ)x is what I would like to obtain. Thanks in advance! Best regards Lance On Monday, July 24, 2023 at 7:24:53 PM UTC+2 Lance Zhang wrote: > Hello Wolfgang, > > thanks for your reply. > > I will follow your point to see if I could find the solution.

Re: [deal.II] Question about how to get the Stiffness matrix partial derivative with respect to density

2023-07-24 Thread Lance Zhang
Hello Wolfgang, thanks for your reply. I will follow your point to see if I could find the solution. One moire question,how could I get ∂A(θ)/∂θx,because I did not find any information about density vector like θ=[θ1,θ2,...,θm],may I know if I have to set density vector value in this finite

Re: [deal.II] Question about how to get the Stiffness matrix partial derivative with respect to density

2023-07-24 Thread Wolfgang Bangerth
The given conditions are stiffness matrix,destination function and x from Ax=b,x is movement ,b is force,A is global stiffness matrix. J(x)=||x||norm-1 This is a questionable choice because dJ/dx is not defined at x=0. There is one equation: dJ(x,θ)/dθ=∂J(x,θ)/∂θ+∂J(x,θ)/∂x *∂x/∂θ=∂J(x,θ)/∂

[deal.II] Question about how to get the Stiffness matrix partial derivative with respect to density

2023-07-24 Thread Lance Zhang
Hello , Thanks for your time to see this question. The given conditions are stiffness matrix,destination function and x from Ax=b,x is movement ,b is force,A is global stiffness matrix. J(x)=||x||norm-1 There is one equation: dJ(x,θ)/dθ=∂J(x,θ)/∂θ+∂J(x,θ)/∂x *∂x/∂θ=∂J(x,θ)/∂θ+∂J(x,θ)/∂x*[A^-1(