# What is the difference between direct and iterative solver?

Table of Contents

- 1 What is the difference between direct and iterative solver?
- 2 What are direct solvers?
- 3 What is a solver in FEA?
- 4 What is solver FEA?
- 5 What is the difference between FEM and FEA?
- 6 Which solver does Ansys?
- 7 What is the difference between direct solver and iterative solver?
- 8 What is the difference between direct and iterative linear systems?

## What is the difference between direct and iterative solver?

In contrast to the direct solver, the iterative solver starts by assuming an approximate solution for the unknowns {u}. The solution is iterated upon to reach an “exact” solution. The purpose of a helmet is to protect the person who wears it from a head injury during impact.

**What is an iterative solver?**

The iterative solver can be used to solve the linear system of algebraic equations that arises at each iteration of the Newton procedure. However, the convergence of the nonlinear problem will be affected by the convergence of the iterative linear solver.

### What are direct solvers?

A direct solver gives the exact solution to the system of equations that define the FE model. So for a system represented by , the exact solution is where is the inverse matrix. Direct solvers don’t usually use this method since computing the inverse of a matrix is computationally very expensive.

**When should we use direct solver?**

Direct Solver: As this method involves inverting the matrix, it is mostly preferred for computationally less expensive problems. From literature, I understand that direct solvers are effective for problems with less than 100,000 unknowns.

#### What is a solver in FEA?

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 direct sparse solver?**

The direct solver, Direct Sparse, solves the set of equations directly without any approximations and hence there are no errors associated with the solution process. There will still be discretization errors which are present both in iterative or direct solvers.

## What is solver FEA?

**What is the solver used in Ansys?**

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.

### What is the difference between FEM and FEA?

FEM: Developed by engineers in the mid-1950s, FEM provides a numerical solution for a complex problem, which allows for some level of error. FEA: The mathematical equations behind FEM are applied to create a simulation, or what’s known as a finite element analysis (FEA).

**What is the difference between the direct sparse and the FFE plus solvers?**

The iterative solver, FFEPlus, uses approximate techniques to solve the problem. It assumes a solution and then calculates the associated errors. The direct solver, Direct Sparse, solves the set of equations directly without any approximations and hence there are no errors associated with the solution process.

#### Which solver does Ansys?

Most beginning ANSYS users should use either the sparse solver or the PCG solver.

**What are solvers in FEA?**

Generally, two types of solvers exist: a direct solver, which is based on the Gauss elimination or LU decomposition; and an iterative solver in which errors are minimized and solutions are converged through iterative calculations.

## What is the difference between direct solver and iterative solver?

Direct methods are bound to give a solution whereas Iterative methods may lead to convergence issues. A direct solver gives the exact solution to the system of equations that define the FE model. So for a system represented by [ K] x → = b →, the exact solution is x → = [ K] − 1 b → where [ K] − 1 is the inverse matrix.

**What is the difference between direct method and iterative method?**

In direct method an exact solution can be obtained in a finite number of operations. While in iterative methods we start with some initial approximation and generate successively improved approximations in an infinite sequence whose limit is the exact solution.

### What is the difference between direct and iterative linear systems?

The end result is that CG is used as an iterative method for large linear systems today. The second big difference is that, for a direct method, you generally need to have the entire matrix stored in memory.

**What are the two types of solvers?**

Generally, two types of solvers exist: a direct solver, which is based on the Gauss elimination or LU decomposition; and an iterative solver in which errors are minimized and solutions are converged through iterative calculations.