The (equation) solver “cracks” the sometimes enormous system of equations which is behind a FEM-model. Equation systems with 10 million equations and more are not unimaginable and also not unsolvable. Of course the solving of that large systems requires a great amount of time and is not always necessary. If it is, the calculation time can be reduced significantly by applying some tricks. For example, a FE-calculation can be accelerated by including the boundary conditions during the saving of the total stiffness matrix or the parallel computing on several CPUs.
The first result of a solver always contains the displacements of the single nodes. In the next step distortions, stresses and nodal forces can be calculated. Besides mechanical quantities, also thermic, electric or magnetic quantities can be calculated if correspondingly a thermic or electromagnetic solver is used. At the end of a calculation, the results are forwarded to the post-processor of the FE-program.