Related papers: An Isogeometric Tearing and Interconnecting (IETI)…
Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…
In recent papers the author introduced a simple alternative to isoparametric finite elements of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…
The construction of volumetric parametrizations for computational domains is a key step in the pipeline of isogeometric analysis. Here, we investigate a solution to this problem based on the mesh deformation approach. The desired domain is…
A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…
This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby…
In this paper, partially invariant solutions (PISs) method is applied in order to obtain new four-dimensional Einstein Walker manifolds. This method is based on subgroup classification for the symmetry group of partial differential…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…
In this work, we present an adjoint-based method for discovering the underlying governing partial differential equations (PDEs) given data. The idea is to consider a parameterized PDE in a general form and formulate a PDE-constrained…
The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the…
A conforming discontinuous Galerkin finite element method is introduced for solving the biharmonic equation. This method, by its name, uses discontinuous approximations and keeps simple formulation of the conforming finite element method at…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…