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We present and analyze a non-standard finite element method based on element-local boundary integral operators that permits polyhedral element shapes as well as meshes with hanging nodes. The method employs elementwise PDE-harmonic trial functions and can thus be interpreted as a local Trefftz method. The construction principle requires the explicit… (More)

The dynamics of beams that undergo large displacements is analyzed in frequency domain and comparisons between models derived by isogeometric analysis and p-FEM are presented. The equation of motion is derived by the principle of virtual work, assuming Timoshenko's theory for bending and geometrical type of nonlinearity. As a result, a nonlinear system of… (More)

We present an algorithm for the approximation of bivariate functions by " low-rank splines " , that is, sums of outer products of univariate splines. Our approach is motivated by the Adaptive Cross Approximation (ACA) algorithm for low-rank matrix approximation as well as the use of low-rank function approximation in the recent extension of the chebfun… (More)

We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. We observe that the performance of standard V-cycle iteration is highly dependent on the spatial dimension as well as the spline degree of the discretization space. Conjugate gradient… (More)

We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. In particular, we study a smoother which incorporates the inverse of the mass matrix as an iteration matrix, and which we call mass-Richardson smoother. We perform a rigorous analysis… (More)

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