@article{WagnerPinskyMalhotra, author = {Wagner, Marcus and Pinsky, Peter M. and Malhotra, Manish}, title = {A multiple-frequency partial-field method for exterior acoustics based on Pad{\´e} via lanczos approximants}, series = {Proceedings of the ASME Noise Control and Acoustics Division - 2001 : presented at the 2001 ASME International Mechanical Engineering Congress and Exposition, November 11 - 16, 2001, New York, New York}, journal = {Proceedings of the ASME Noise Control and Acoustics Division - 2001 : presented at the 2001 ASME International Mechanical Engineering Congress and Exposition, November 11 - 16, 2001, New York, New York}, number = {28}, publisher = {ASME}, address = {New York, NY}, isbn = {0-7918-3551-0}, doi = {10.1115/IMECE2001/NCA-23524}, pages = {229 -- 234}, abstract = {A solution methodology is introduced for the efficient computation of the acoustic field over restricted domains and for a frequency window. Typically, such partial field solutions include, for example, surfaces enclosing the radiating structure or even single points in the computational domain. The multiple-frequency partial-field (MFPF) method starts out by reformulating the finite element matrix system into a suitable shifted form. The DtN map is used as a radiation boundary condition and is interpreted as a low rank update of the matrix problem. The shifted standard form is then approximated by a rational matrix-valued Pad{\´e} approximant and solved simultaneously over a frequency range. To obtain the Pad{\´e} approximation, a banded unsymmetric Lanczos process is applied on the standard shifted form exploiting the matrix Pad{\´e}-via-Lanczos connection. Numerical examples show the feasibility of the outlined procedure.}, language = {en} }