Related papers: Higher-continuity s-version of finite element meth…
Easy to construct and optimally convergent generalisations of B-splines to unstructured meshes are essential for the application of isogeometric analysis to domains with non-trivial topologies. Nonetheless, especially for hexahedral meshes,…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…
This work develops an elasto-plastic cell-based smoothed finite element method (CSFEM) for geotechnical analysis. The formulation incorporates a smoothed strain field into the standard elasto-plastic framework based on the Mohr-Coulomb…
In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…
We present a new refinement strategy for locally refined B-splines which ensures the local linear independence of the basis functions. The strategy also guarantees the spanning of the full spline space on the underlying locally refined…
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 present a boundary-spheropolygon element method (BSEM), that combines the boundary integral method (BIM) and the spheropolygon-based discrete element method (SEM). The interaction between particles is simulated via the SEM, and the…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM…
In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-GFEM) developed in [I. Babu\v{s}ka and R. Lipton, Multiscale Modeling and Simulation 9 (2011), pp. 373--406]. We outline the numerical implementation of…
We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
This paper presents a product to sum approach for a fast and efficient matrix filling in a hierarchical finite-element method (FEM). Due to the existence of a coupling factor arising from the material and Jacobian inhomogeneities in curved…
In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to…
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial…