@Article{icces.2023.09441,
AUTHOR = {Qingyuan	Hu, Yuan Liang},
TITLE = {The Nitsche’s Method and Applications in Isogeometric	Analysis},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {27},
YEAR = {2023},
NUMBER = {3},
PAGES = {1--2},
URL = {http://www.techscience.com/icces/v27n3/55166},
ISSN = {1933-2815},
ABSTRACT = {The	Nitsche’s	method	is	originally	proposed	as	a	technique	to	impose	boundary	conditions,	nowadays	it	is	
widely	used	for	isometric	analysis	(IGA)	and	corresponding	topology	optimization	applications.	Based	on	
our	previous	research	[1],	we	present	a	simple	way	to	derive	the	Nitsche’s	formulations	for	different	kind	of	
boundary	and	interface	conditions,	and	studied	this	technique	in	the	context	of	IGA	discretization,	especially	
for	 patch	 coupling	 and	 contact	 problems.	 The	 skew-symmetric	 variant	 of	 the	 Nitsche’s	 method	 is	 then	
further	studied.	For	linear	boundary	or	interface	conditions,	the	skew-symmetric	formulation	is	parameterfree.	For	contact	conditions,	it	remains	stable	and	accurate	for	a	wide	range	of	the	stabilization	parameter.	
Topological	optimization	plays	a	guiding	role	in	the	conceptual	design	process.	For	multi-patch	models	in	
engineer	practices,	the Nitsche’s	method	is	used	to	glue	different	meshes	to	perform	multi-patch	IGA	and	
then	 topology	 optimization	 [2].	 The	 discrete	 variable	 topology	 optimization	 algorithm	 based	 on	integer	
programming	 is	 adopted	 in	 order	 to	 obtain	 clear	 boundaries	 for	 topology optimization	 [3,4].	 Taking	
advantages	of	curved-edge	elements	in	IGA,	topology	optimization	in	the	framework	of	IGA	can	obtain	locally	
smoother	material	boundaries	than	traditional	FEM	under	the	same	level	of	mesh	resolution.	In	addition,	in	
order	to	accelerate	the	computational	process	with	extremely	large	amount	of	degrees	of	freedom	and	get	
high-resolution	results,	we	extend	our	study	to	the	PETSc	framework	with	high	performance	clusters.},
DOI = {10.32604/icces.2023.09441}
}