An Object Oriented, Finite Element Framework for Linear Wave Equations
Abstract
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
 Authors:
 Univ. of California, Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 15014610
 Report Number(s):
 UCRLTH206232
TRN: US200807%%736
 DOE Contract Number:
 W7405ENG48
 Resource Type:
 Thesis/Dissertation
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACOUSTICS; CALCULI; ELASTICITY; ELECTRODYNAMICS; FINITE ELEMENT METHOD; MAGNETOHYDRODYNAMICS; SCALARS; VECTORS; WAVE EQUATIONS
Citation Formats
Koning, Joseph M. An Object Oriented, Finite Element Framework for Linear Wave Equations. United States: N. p., 2004.
Web. doi:10.2172/15014610.
Koning, Joseph M. An Object Oriented, Finite Element Framework for Linear Wave Equations. United States. doi:10.2172/15014610.
Koning, Joseph M. Mon .
"An Object Oriented, Finite Element Framework for Linear Wave Equations". United States.
doi:10.2172/15014610. https://www.osti.gov/servlets/purl/15014610.
@article{osti_15014610,
title = {An Object Oriented, Finite Element Framework for Linear Wave Equations},
author = {Koning, Joseph M.},
abstractNote = {This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.},
doi = {10.2172/15014610},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Mar 01 00:00:00 EST 2004},
month = {Mon Mar 01 00:00:00 EST 2004}
}

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