Infinite element method: Difference between revisions

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{{Differential equations}}

The '''infinite element method''' is a [[numerical analysis|numerical method]] for solving problems of engineering and [[mathematical physics]]. It is a modification of [[finite element method]]. The method divides the ___domain concerned into infinitely many sections. In the first instance this results in an infinite set of equations, which is then reduced to a finite set.<ref>{{Cite book|title=Infinite Element Methods|last=Ying|first=Lung-an|publisher=|year=1995|isbn=978-3-528-06610-9|___location=|pages=}}</ref> The method is commonly used to solve acoustic problems. <ref>{{Cite book | doi=10.1007/978-94-015-9095-2_15|chapter = Infinite Element Methods|title = IUTAM Symposium on Computational Methods for Unbounded Domains| volume=49| pages=143–150|series = Fluid Mechanics and its Applications|year = 1998|last1 = Gerdes|first1 = K.| isbn=978-90-481-5106-6}}</ref><ref>{{Cite journal |last=Autrique |first=Jean-Christophe |last2=Magoulès |first2=Frédéric |date=July 2006 |title=Studies of an infinite element method for acoustical radiation |journal=Applied Mathematical Modelling |volume=30 |issue=7 |pages=641–655 |doi=10.1016/j.apm.2005.08.022 |issn=0307-904X}}</ref>

The '''infinite element method''' is a [[numerical analysis|numerical method]] for solving problems of engineering and [[mathematical physics]]. It is a modification of [[finite element method]]. The method divides the ___domain concerned into infinitelysections manyof sectionsinfinite length. In thecontrast firstwith instancea thisfinite resultselement inwhich anis infiniteapproximated setby ofpolynomial equationsexpressions on a finite support, whichthe unbounded length of the infinite element is thenfitted reducedwith tofunctions aallowing finitethe evaluation of the field at the asymptote. The number of functions and points of interpolations define the accuracy of the element in the infinite setdirection.<ref>{{Cite book|title=Infinite Element Methods|last=Ying|first=Lung-an|publisher=|year=1995|publisher=Peking University Press |isbn=978-3-528-06610-9|___location=|pages=}}</ref> The method is commonly used to solve acoustic problems and allows to respect the [[Sommerfeld radiation condition|Sommerfeld]] condition of non-return of the acoustic waves and the diffusion of the pressure waves in the far field. <ref>{{Cite book | doi=10.1007/978-94-015-9095-2_15|chapter = Infinite Element Methods|title = IUTAM Symposium on Computational Methods for Unbounded Domains| volume=49| pages=143–150|series = Fluid Mechanics and its Applications|year = 1998|last1 = Gerdes|first1 = K.| isbn=978-90-481-5106-6}}</ref><ref>{{Cite journal |lastlast1=Autrique |firstfirst1=Jean-Christophe |last2=Magoulès |first2=Frédéric |date=July 2006 |title=Studies of an infinite element method for acoustical radiation |journal=Applied Mathematical Modelling |volume=30 |issue=7 |pages=641–655 |doi=10.1016/j.apm.2005.08.022 |issn=0307-904X|doi-access=free }}</ref>

==References==

{{Reflist}}

{{Numerical PDE}}

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[[Category:Continuum mechanics]]