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How do you use Thomas algorithm?
The Thomas algorithm consists of two steps. In Step 1 decomposing the matrix into M = LU and solving Lρ = r are accomplished in a single downwards sweep, taking us straight from Mx = r to Ux = ρ. In step 2 the equation Ux = ρ is solved for x in an upwards sweep.
Which method converges fast to solution?
Newton’s Method is a very good method When the condition is satisfied, Newton’s method converges, and it also converges faster than almost any other alternative iteration scheme based on other methods of coverting the original f(x) to a function with a fixed point.
Which is the correct method for two grid multigrid?
Be carefuly on the value on the boundary points. Code the two-grid method. On the fine grid, apply m times G-S iteration and then restrict the updated residual to the coarse grid. On the coarse grid, use G-S iteration or direct method to solve the equation below the discretization error.
How to implement the non recrusive V-cycle in multigrid?
Store the smoother tril (A) and triu (A) in each level. Follow the lecture notes Introduction to Multigrid method to implement the non-recrusive V-cycle. Be careful on the boundary nodes. Restrict smoothing to interiori nodes only and enforce the residual on boundary nodes to be zero.
Which is a compact recursive definition in multigrid methods?
It belongs to a family of multigrid methods, the so-called multigrid methods with γ-cycle that have the following compact recursive definition: v h←M γ (vh,fh) 1. Pre smoothing: Apply the smoother ν. 1 times to Ahuh = fh with the initial guess vh. 2. If Ωh is the coarsest grid −solve the problem.
What do pro and ISC mean in multigrid?
In the input, A is a SPD matrix and isC is a logical array to indicate nodes in coarse matrix. In the output Pro and Res are prolongation and restriction matrices satisfying Res = Pro’.