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Using an elegant mixture of geometry, graph theory and linear
analysis, this monograph completely solves a problem lying at the
interface of Isogeometric Analysis (IgA) and Finite Element Methods
(FEM). The recent explosion of IgA, strongly tying Computer Aided
Geometry Design to Analysis, does not easily apply to the rich
variety of complex shapes that engineers have to design and
analyse. Therefore new developments have studied the extension of
IgA to unstructured unions of meshes, similar to those one can find
in FEM. The following problem arises: given an unstructured planar
quadrilateral mesh, construct a C1-surface, by piecewise Bezier or
B-Spline patches defined over this mesh. This problem is solved for
C1-surfaces defined over plane bilinear Bezier patches, the
corresponding results for B-Splines then being simple consequences.
The method can be extended to higher-order quadrilaterals and even
to three dimensions, and the most recent developments in this
direction are also mentioned here.
th This volume contains a selection of 41 refereed papers presented
at the 18 International Conference of Domain Decomposition Methods
hosted by the School of ComputerScience and Engineering(CSE) of the
Hebrew Universityof Jerusalem, Israel, January 12-17, 2008. 1
Background of the Conference Series The International Conference on
Domain Decomposition Methods has been held in twelve countries
throughout Asia, Europe, the Middle East, and North America,
beginning in Paris in 1987. Originally held annually, it is now
spaced at roughly 18-month intervals. A complete list of past
meetings appears below. The principal technical content of the
conference has always been mathematical, but the principal
motivation has been to make ef cient use of distributed memory
computers for complex applications arising in science and
engineering. The leading 15 such computers, at the "petascale"
characterized by 10 oating point operations per second of
processing power and as many Bytes of application-addressablem-
ory, now marshal more than 200,000 independentprocessor cores, and
systems with many millions of cores are expected soon. There is
essentially no alternative to - main decomposition as a stratagem
for parallelization at such scales. Contributions from
mathematicians, computerscientists, engineers, and scientists are
together n- essary in addressing the challenge of scale, and all
are important to this conference.
th This volume contains a selection of 41 refereed papers presented
at the 18 International Conference of Domain Decomposition Methods
hosted by the School of ComputerScience and Engineering(CSE) of the
Hebrew Universityof Jerusalem, Israel, January 12-17, 2008. 1
Background of the Conference Series The International Conference on
Domain Decomposition Methods has been held in twelve countries
throughout Asia, Europe, the Middle East, and North America,
beginning in Paris in 1987. Originally held annually, it is now
spaced at roughly 18-month intervals. A complete list of past
meetings appears below. The principal technical content of the
conference has always been mathematical, but the principal
motivation has been to make ef cient use of distributed memory
computers for complex applications arising in science and
engineering. The leading 15 such computers, at the "petascale"
characterized by 10 oating point operations per second of
processing power and as many Bytes of application-addressablem-
ory, now marshal more than 200,000 independentprocessor cores, and
systems with many millions of cores are expected soon. There is
essentially no alternative to - main decomposition as a stratagem
for parallelization at such scales. Contributions from
mathematicians, computerscientists, engineers, and scientists are
together n- essary in addressing the challenge of scale, and all
are important to this conference.
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