This review paper collects several results that form part of the theoretical foundation of
isogeometric methods. We analyse variational techniques for the numerical resolution of …

We compare isogeometric collocation with isogeometric Galerkin and standard C 0 finite
element methods with respect to the cost of forming the matrix and residual vector, the cost …

We consider large linear systems arising from the isogeometric discretization of the Poisson
problem on a single-patch domain. The numerical solution of such systems is considered a …

We consider fast solvers for large linear systems arising from the Galerkin approximation
based on B-splines of classical d-dimensional elliptic problems, d≥ 1, in the context of …

We consider the stiffness matrices arising from the Galerkin B-spline isogeometric analysis
discretization of classical elliptic problems. By exploiting their specific spectral properties …

A balancing domain decomposition by constraints (BDDC) preconditioner with a novel
scaling, introduced by Dohrmann for problems with more than one variable coefficient and …

We present (geometric) multigrid methods for isogeometric discretization of scalar second
order elliptic problems. The smoothing property of the relaxation method, and the …

In this paper we study how the use of a more continuous set of basis functions affects the
cost of solving systems of linear equations resulting from a discretized Galerkin weak form …

In this theoretical study, we explore how to automate the selection of weights and primal
constraints in BDDC methods for general SPD problems. In particular, we address the three …

In the 1970s during decomposition of hydrocarbons, small diameter carbon fibers were
observed, but because of limitation on characterization and measurement they were not …