Contents
What is an ill-conditioned problem?
In non-mathematical terms, an ill-conditioned problem is one where, for a small change in the inputs (the independent variables) there is a large change in the answer or dependent variable. This means that the correct solution/answer to the equation becomes hard to find.
What is difference between direct and iterative method?
Direct methods compute the solution to a problem in a finite number of steps. In contrast to direct methods,iterative methodsare not expected to terminate in a number of steps. Starting from an initial guess, iterative methods form successive approximations thatconvergeto the exact solution only in the limit.
How do you tell if a system is ill-conditioned?
Which is better an iterative solver or a direct solver?
The big advantage of the iterative solvers is their memory usage, which is significantly less than a direct solver for the same sized problems. The big disadvantage of the iterative solvers is that they do not always “just work”.
Why is convergence slower in an iterative solver?
If you are working on problems that are not as well-conditioned, then the convergence will be slower. Oscillatory behavior of an iterative solver is often an indication that the problem is not properly set up, such as when the problem is not sufficiently constrained. A typical convergence graph for an iterative solver is shown below:
When does an iterative solver have an oscillatory behavior?
Oscillatory behavior of an iterative solver is often an indication that the problem is not properly set up, such as when the problem is not sufficiently constrained. A typical convergence graph for an iterative solver is shown below: By default, the model is considered converged when the estimated error in the iterative solver is below 10 -3.
What are the disadvantages of iterative solvers in physics?
The big disadvantage of the iterative solvers is that they do not always “just work”. Different physics do require different iterative solver settings, depending on the nature of the governing equation being solved. Luckily, COMSOL already has built-in default solver settings for all predefined physics interfaces.