Disclosed are techniques for representing and modeling one or more systems
in which each system corresponds to an application mode. This may be done
for one or more geometries using local and/or non-local couplings. For
each application mode, physical quantities are modeled and may be defined
using a graphical user interface. Physical properties may be used to
model the physical quantities of each system. The physical properties may
be defined in terms of numerical values or constants, and mathematical
expressions that may include numerical values, space coordinates, time
coordinates, and actual physical quantities. Physical quantities and any
associated variables may apply to some or all of a geometric domain, and
may also be disabled in other parts of a geometrical domain. Partial
differential equations describe the physical quantities. One or more
application modes may be combined using an automated technique into a
combined system of partial differential equations as a multiphysics
model. A portion of the physical quantities and variables associated with
the combined system may be selectively solved for. The partial
differential equations may be displayed and may in turn solve for the
system of partial differential equations in accordance with a general
form or a coefficient form. An automated technique provides for automatic
derivation of the combined partial differential equations and boundary
conditions. This technique automatically merges the equations from a
plurality of application modes, and in some instances, performs symbolic
differentiation of the equations, producing a single system of partial
differential equations. A subset of physical quantities and associated
variables not solved for may be used as initial values to the system of
partial differential equations.