ABSTRACT
This chapter discusses volume and surface integrals over the regions of triangular meshes. These quantities can be used to determine inductances, capacitances, and forces. Volume integrals are useful when we know the distribution of current or space-charge over a spatial region. The chapter derives expression for magnetic field energy density and applies volume integrals to find field energy in regions of a solution space. It reviews capacitance calculations from electrostatic solutions including mutual capacitances between multiple electrodes. The chapter describes the methods to find self- and mutual inductances in systems with arbitrary sets of coils. It covers techniques to find electric and magnetic forces on rigid body regions. The chapter reviews particle orbit tracking in vacuum using numerical field solutions. It extends the methods to the design of high-current electron and ion guns where the particles make significant contributions to the field solution. The chapter describes simulations of the response of Hall-effect probes, devices used for magnetic field measurements.
