Recent content by FrankST

Thanks bigfooted for your response. The reason I want to solve it using segregated method is for memory storage issue. For example, in case of 10 coupled PDE I am dealing with 100,000 x 100,000 matrix and I need to save memory. Thanks again for your attention.

All, I have a system of three coupled PDE and I discretized the equations using finite difference method. It results in a block matrix equations as: [A11 A12 A13] [x1] = [f1] [A21 A22 A23] [x2] = [f2] [A31 A32 A33] [x3] = [f3] where, any of Aij is a square matrix. I use...

About the relaxation method: I can't get the step 2. After assuming some value for the nodes in step 1 I would require to solve Eq1 for f1. Then when should I take the average of the surrounding nodes? What I can think is that after solving Eq1 for f1 I should update the nodal values for...

Maybe this is what you're meaning: (a_1f,xx+a_2f,yy+a_3g,xx+a_4g,yy-a_5f-a_6g)^2+(b_1f,xx+b_2f,yy+b_3g,xx+b_4g,yy-b_5f-b_6g)^2=0 \Rightarrow (a_1f,xx+a_2f,yy+a_3g,xx+a_4g,yy-a_5f-a_6g)=+(b_1f,xx+b_2f,yy+b_3g,xx+b_4g,yy-b_5f-b_6g) and...

First of all, thanks a lot for your attention to this problem. Back to the problem, You squared each equation and you summed them up. Then you used FD equivalent to discretize the equations. What I can't understand is that after replacing FD formulas inside the expression with...

I've already explained the problem. Do you have any idea on another method to solve the equations?

It is related to the deformation that two indentors make in an elastic membrane.

The constant coefficients are sometimes in a way that makes the system singular. So in most cases if I want to solve the system with no iteration (in the sense I mentioned in the first post) I end up with a singular system of equations. Let me rewrite the system in in actual forms: 1- a1 *...

Thanks a lot for your valuable information. I tried an analytical solution first but due to geometry of the domain (there are some holes inside the rectangular domain where I have Dirichlet BCs) I decided to use a numerical method and FDM is my current option. In the iterative method that...

By solving a system I do mean finding f(x,y) and g(x,y) that satisfy the PDE system I showed. I have a rectangular domains with thousands of nodes (discretized domain). I need to find f and g at each node. Therefore, I am dealing with a system of equations (after discretization) consisting of...

Thanks for your answer. But I am not sure if I understood your method. I can't see any g(x,y) in your solution. I have two unknown functions called f(x,y) and g(x,y). I need to find these two functions by solving the system of PDE I mentioned earlier. My question was that if there is a...

All, As part of my research I came up with a boundary value problem where I need to solve the following system of coupled PDE: 1- a1 * f,xx + a2 * f,yy + a3 * g,xx + a4 * g,yy - a5 * f - a6 * g = 0 2- b1 * f,xx + b2 * f,yy + b3 * g,xx + b4 * g,yy - b5 * f - b6 * g = 0 Where, ai's...

Dear All, I have a linear system of equations such as Ax = b where A is a m-by-n matrix and m < n and A is a full rank matrix (rank(A) = m). Since there are infinitely many solutions to this problem, I was looking for different methods to solve this problem. As I understood I can pose this...

Hi, I have a system of coupled ODE like: a1 * Y1" + a2 * Y2" + b1 * Y1 + b2 * Y2 = 0 a2 * Y1" + a3 * Y2" + b2 * Y1 + b3 * Y2 = 0 I know for example by eigenvalue method I can solve it, but here is the issue: Y1 = f1 (x - a) and Y2 = f2 ( x - b). In the other word there is a shift...

Thanks a lot.