Related papers: Isogeometric Mortar Coupling for Electromagnetic P…
For Kichhoff-Love shell problems a new mixed formulation solely based on standard $H^1$ spaces is presented. This allows for flexibility in the construction of discretization spaces, e.g., standard $C^0$-coupling of multi-patch isogeometric…
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied…
This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices}…
This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation.…
In the context of isogeometric analysis, globally $C^1$ isogeometric spaces over unstructured quadrilateral meshes allow the direct solution of fourth order partial differential equations on complex geometries via their Galerkin…
We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…
In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
We consider heterogeneous coupling problems on an abstract level, establishing fundamental principles of domain decomposition agnostic to the solvers of the local subproblems. Introducing a coupling framework reminiscent of FETI methods,…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Isogeometric approach applied to Boundary Element Methods is an emerging research area. In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk and a novel choice of interface conditions with additional…
Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…
No positive result has been obtained on the magnetic monopoles search. This allows to consider different theoretical approaches as the proposed in this paper, developed in the framework of the Einstein General Relativity. The properties of…