What are direct solvers?

What are direct solvers?

The direct solvers used by COMSOL are the MUMPS, PARDISO, and SPOOLES solvers. These solvers will all arrive at the same answer for all well-conditioned finite element problems, which is their biggest advantage, and can even solve some quite ill-conditioned problems.

What is mumps Comsol?

MUMPS (MUltifrontal Massively Parallel sparse direct Solver) is a software application for the solution of large sparse systems of linear algebraic equations on distributed memory parallel computers. It was developed in European project PARASOL (1996–1999) by CERFACS, IRIT-ENSEEIHT and RAL.

What is the difference between direct and iterative methods?

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 does FEA solvers work?

what is an FEA solver ? Well, basically, every FEA software is composed of 3 parts the Pre, the Post and the solver. The job of the solver is to take these input data, to process them using specific algorithms (I will detail that a bit later) and to give an output that correspond to the result of the analysis.

What is Spooles?

SPOOLES is a library for solving sparse real and complex linear systems of equations, written in the C language using object oriented design. Solve square linear systems using a variety of Krylov iterative methods. The preconditioner is a drop tolerance factorization, constructed with or without pivoting for stability.

What solver does Ansys use?

ANSYS frontal solver
ANSYS frontal solver. The original solver used in ANSYS is the frontal solver, a direct Cholesky factorization algorithm [5, 6]. This direct factorization method was designed for computers with very limited memory but remained an efficient direct method for many years.

Why iterative methods are important?

A major advantage of iterative methods is that roundoff errors are not given a chance to “accumulate,” as they are in Gaussian Elimination and the Gauss-Jordan Method, because each iteration essentially creates a new approximation to the solution.

What is difference between direct and indirect linear algebraic equation?

“Direct” techniques use a “formula”, whereas “indirect” techniques iterate until convergence. Same thing for the solutions of ordinary linear differential equations—which have direct “formulas” in terms of complex exponentials—and other systems, which don’t.

Why FEA is widely accepted in engineering?

Useful in structural, vibration, and thermal analysis, FEA has been widely implemented by automotive companies. When used properly, the FEA becomes a tremendous productivity tool, helping design engineers reduce product development time and cost.

What is an iteration matrix?

Definition. An iterative method is defined by. and for a given linear system with exact solution the error by. An iterative method is called linear if there exists a matrix such that. and this matrix is called the iteration matrix.

Which is better COMSOL or iterative solvers for linear equations?

When solving the systems of linear equations of a simulation, COMSOL will automatically detect the best solver without requiring any user interaction. The direct solvers will use more memory than the iterative solvers, but can be more robust.

How are direct solvers different from other solvers?

The direct solvers differ primarily in their relative speed. The MUMPS, PARDISO, and SPOOLES solvers can each take advantage of all of the processor cores on a single machine, but PARDISO tends to be the fastest and SPOOLES the slowest. SPOOLES also tends to use the least memory of all of the direct solvers.

Are there any direct methods for solving a system?

There are two basic classes of methods for solving system ( 4.6 ). The first class is represented by direct methods. They theoretically give an exact solution in a (predictable) finite number of steps.

What kind of algorithms are used to solve for linear systems?

There are two fundamental classes of algorithms that are used to solve for : direct and iterative methods. We will introduce both of these methods and look at their general properties and relative performance, below. The direct solvers used by COMSOL are the MUMPS, PARDISO, and SPOOLES solvers.