Related papers: Isogeometric Analysis and Harmonic Stator-Rotor Co…
We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The…
Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are…
The isomorphism problem means to decide if two given finite-dimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational…
We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…
Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with…
In this paper, a recently developed Higher Order Microplane (HOM) model for softening and localization, is implemented within a isogeometric finite element framework. The HOM model was derived directly from a three dimensional discrete…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
While interpolatory bases such as the Lagrange basis form the cornerstone of classical finite element methods, they have been replaced in the more general finite element setting of isogeometric analysis in favor of other desirable…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the…
The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard…
In computational anatomy, the statistical analysis of temporal deformations and inter-subject variability relies on shape registration. However, the numerical integration and optimization required in diffeomorphic registration often lead to…
We use the alternating direction method to simulate implicit dynamics. ur spatial discretization uses isogeometric analysis. Namely, we simulate a (hyperbolic) wave propagation problem in which we use tensor-product B-splines in space and…
In order to perform isogeometric analysis with increased smoothness on complex domains, trimming, variational coupling or unstructured spline methods can be used. The latter two classes of methods require a multi-patch segmentation of the…
The simulation of three dimensional magnetostatic problems plays an important role, for example when simulating synchronous electric machines. Building on prior work that developed a domain decomposition algorithm using isogeometric…
Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
In this paper, a novel isogeometric method for Biot's consolidation model is constructed and analyzed, using a four-field formulation where the unknown variables are the solid displacement, solid pressure, fluid flux, and fluid pressure.…
We consider a Johnson-N\'ed\'elec FEM-BEM coupling, which is a direct and non-symmetric coupling of finite and boundary element methods, in order to solve interface problems for the magnetostatic Maxwell's equations with the magnetic vector…