# Global quantities

## Definition

The global quantities are the quantities that result from the integration of local quantities on the entire or only a part of the computation domain.

The global quantities are of a great interest, because they often represent measurable quantities, and therefore significant for the performance of the studied device.

## From the physical application perspective …

From the physical application perspective, the global quantities depend on the current physical application*.

In case of a magnetic application , the significant global quantities are the magnetic force, the magnetic torque, the magnetic energy, the magnetic flux through a coil, …

In case of an electric application , the significant global quantities are the electric field, the electrostatic force, the electric energy, …

In case of a thermal application, the significant global quantities are the heat fluxes, …

Note: *A detailed list of the total quantities available for each physical application is presented in volume 3 of this guide (§ related to the active physical application).

## From a mathematical perspective

From a mathematical perspective, the global quantities are scalar or vector, real or complex quantities.

## From a finite element analysis perspective …

From a finite element analysis perspective, the global quantities are obtained by the integration of local quantities on the entire or only a part of the computation domain.

For all the meshed regions, the integration of a quantity is carried out element by element; for each element, several points of integration are taken into account. The process used is the Gauss method, which ensures a high degree of accuracy with a reduced number of computations.

The precision one can expect from a finite elements analysis is not the same for local or global quantities. The estimation of global quantities is generally performed with better precision.