# Finite Element Method Solved Problems For large models, inverting the matrix is highly expensive and will require advanced iterative solvers (over standard direct solvers).

These solutions are unconditionally stable and facilitate larger time steps.

Despite this advantage, the implicit methods can be extremely time-consuming when solving dynamic and nonlinear problems.

Explicit FEM is used to calculate the state of a given system at a different time from the current time.

In contrast, an implicit analysis finds a solution by solving an equation that includes both the current and later states of the given system.

Some interesting examples are also depicted in Figure 01.

All of these problems are expressed through mathematical partial differential equations (PDE’s).

For all nonlinear and non-static analyses, incremental load (also known as displacement steps) are needed.

In more simplistic terminology, this means we need to break down the physics/time relationship to solve a mathematical problem.

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