HFSS15: Domain Decomposition Method

HFSS solves a linear matrix equation of the form:

(1)

where the excitation vector b is commonly called the right-hand-side or RHS. The number of RHS vectors depends on the total number of modes used to excite the problem.

HFSS provides three distinct solution methods. By default, a direct solver is used and is the preferred method for small to medium size problems and/or problems with a large number of modes. A major strength of the direct solver is the ability to provide a solution for a large number of modes with relatively small computational overhead for the multiple RHS. However, if the problem size is too large for the machine memory, the second option is to use the iterative solver which can handle larger problems but requires a complete solution for each RHS. The iterative solver modifies the matrix equation (1) by multiplying both sides with a pre-conditioner, M, in order to enable a faster solution:

(2)

Both the direct solver and the iterative solver work only with a single machine's shared memory. This limitation is addressed in HFSS with the introduction of an advanced solving technique called the Domain Decomposition Method (DDM) which enables the use of distributed memory across many different machines to solve very large problems.

• Basic DDM Theory

• Computational Memory

• Computational Time