Numerical Solutions
Numerical solutions use a mesh of the structure to perform the simulation. The most popular methods are: Finite difference time-domain (FDTD) method, Finite element Method (FEM) and Method of Moments (MoM).
The finite-difference time-domain (FDTD) method is a robust and popular technique that consists in solving differential equations numerically as well as certain boundary conditions defined by the problem. This is done by discretizing the space and time, and using finite differencing formulas, thus the partial differential equations that describe the physics of the problem can be solved numerically by computer programs.
The Finite Element Method (FEM) is also numerical scheme employed to solve engineering and mathematical problems described by differential equations as well as boundary conditions. It discretizes the space into smaller elements for which basis functions are assigned to their nodes or edges. Basis functions are linear or higher order polynomials. Applying the differential equation and the boundary conditions of the problem to the basis functions, a system of equations is formulated using either the Ritz or Galerkin method. Finally, a direct or iterative method is employed to solve the system of linear equations. For the thermal case, FEM method is more suitable due to the nonlinearity nature of the thermal properties.
Read more about this topic: Thermal Simulations For Integrated Circuits, Techniques To Solve Heat Equation
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