1,721,087 research outputs found
Isogeometric Discrete Differential Forms in Three Dimensions
No full textThe concept of isogeometric analysis (IGA) was first applied to the approximation of Maxwell equations in [A. Buffa, G. Sangalli, and R. Vázquez, Comput. Methods Appl. Mech. Engrg., 199 (2010), pp. 1143–1152]. The method is based on the construction of suitable B-spline spaces such that they verify a De Rham diagram. Its main advantages are that the geometry is described exactly with few elements, and the computed solutions are smoother than those provided by finite elements. In this paper we develop the theoretical background to the approximation of vector fields in IGA. The key point of our analysis is the definition of suitable projectors that render the diagram commutative. The theory is then applied to the numerical approximation of Maxwell source problems and eigenproblems, and numerical results showing the good behavior of the scheme are also presented
Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data
No full textWe study the mixed formulation of the stochastic Hodge-Laplace problem defined on a n-dimensional domain D (n ≥ 1), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We derive and analyze the moment equations, that is the deterministic equations solved by the m-th moment (m ≥ 1) of the unique stochastic solution of the stochastic problem. We find stable tensor product finite element discretizations, both full and sparse, and provide optimal order of convergence estimates. In particular,
we prove the inf-sup condition for sparse tensor product finite element spaces
Mesh generation and numerical analysis of a Galerkin method for hyghly conductive prefractal layers
No full textIn this paper we provide the piecewise linear Galerkin approximation of a second order transmission problem across a highly conductive prefractal layer of von Koch type. We firstly generate an appropriate mesh adapted to the geometric shape of the interface and then we construct a refinement algorithm consistent with a suitable estimate in appropriate weighted Sobolev spaces. We also obtain a quasi-optimal error estimate in the energy norm and finally we demonstrate the validity of our theory through numerical tests
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
No full textIn this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and following the isogeometric paradigm, we map them on domains which are (piecewise) spline or NURBS geometries. We analyze their geometric and topological structure, as related to the connectivity of the underlying mesh, and we present degrees of freedom together with their physical interpretation. The theory is then extended to the case of meshes with T-junctions, leveraging on the recent theory of T-splines. The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose
Analysis of coordination in multi-agent systems through partial difference equations
No full textIn this paper we introduce the framework of Partial difference Equations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with decentralized control schemes. Both leaderless and leader-follower models are considered. PdEs mimic Partial Differential Equations (PDEs) on graphs and can be studied by introducing concepts of functional analysis strongly inspired to the corresponding ones arising in PDEs theory. We generalize different models proposed in the literature by introducing errors in the agent dynamics and analyze agent coordination through the joint use of PdEs and automatic control tools. Moreover, for the simplest control schemes, we show that the resulting PdEs enjoy properties that are similar to those of well-known PDEs like the heat equation, thus allowing to exploit physical-based reasoning for conjecturing formation properties
NURBS-based BEM implementation of high order surface impedance boundary conditions
No full textWhen implementing high order surface impedance
boundary conditions in collocation BEM with constant or linear elements, difficulties arise due to the computation of the curvature of the conductors and of the tangential derivatives of the unknowns. The use of non-uniform rational B-splines overcomes the above problems and gives a better representation of complex geometries. After comparing the previously derived formulation of high order surface impedance boundary conditions with that obtained by other authors following a different approach, the
resulting surface integral equations are discretized using nonuniform rational B-splines. Canonical problems of two circular and elliptical conductors are used for validation. Finally, the problem of the computation of per-unit-length parameters of sector shaped cables is solved, showing the accuracy of the method
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