Moment method (electrical engineering)

The moment method is the name of an integral equation method that is used in high-frequency technology in the field of radiation problems.

To solve a linear operator equation in the form

${\ displaystyle ({\ rm {D}} f (x ')) (x) = g (x) \,}$

is the sum approach first

${\ displaystyle f (x) = \ sum _ {i} I_ {i} b_ {i} (x) \,}$

with the basic functions introduced into this. By multiplying the operator equation with an equally large set of test functions and integrating over the solution domain, a linear system of equations of the form is obtained ${\ displaystyle b_ {i} (x)}$ ${\ displaystyle c_ {j} (x)}$

${\ displaystyle {\ underline {Z}} \ cdot {\ underline {I}} = {\ underline {U}}}$

With

${\ displaystyle ({\ underline {Z}}) _ {ij} = \ int ({\ rm {D}} b_ {i} (x ')) c_ {j} (x) {\ rm {d}} x}$ ,

${\ displaystyle ({\ underline {I}}) _ {j} = I_ {j}}$

and

${\ displaystyle ({\ underline {U}}) _ {j} = \ int g (x) c_ {j} (x) {\ rm {d}} x}$ .

The approximated solution of the operator equation then results directly from the sum approach and the solution of the linear system of equations.

If one starts further , one speaks of the Galerkin procedure . In contrast to the finite element method , however, full-range basis functions can also be used. ${\ displaystyle c_ {j} (x) = b_ {j} (x)}$

The Combined Node Method of Moments (CN-MoM) is an extension of the moment method in which the BEM is combined with partial analytical solutions. Using the CN-MoM significantly reduces the number of unknowns. This reduction in the number of unknowns leads to a considerable reduction in the computing time.

literature

Roger F. Harrington: Field Computation by Moment Methods , The Institute of Electrical and Electronics Engineers, Inc., 1993.
Reza Sabbagh Amirkhizi: EMC analysis of multilayer printed circuit boards with the moment method and hybrid approaches Shaker Verlag 2006, ISBN 978-3-8322-5450-6
Reza Sabbagh Amirkhizi: Combined-Node Moment Method Analysis of Through Hole Vias EMC Zurich 2005
Reza Sabbagh Amirkhizi: Efficient Calculation of Multilayered PCBs by Combining Hybrid Methods with the Method of Moments IEEE EMC Chicago 2005