Related papers: Multiply Periodic Splines
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
We develop a method for the rigorous estimation of Hausdorff dimensions of limit sets produced by continued fraction iterated function systems. Our method is based on the approximation of a Perron-Frobenius operator using the finite element…
The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discretization of thin plate splines. The mixed formulation is…
The immersed isogeometric Boundary Element Method is presented and applied to the simulation of underground excavations. Nonuniform rational B-splines (NURBS) are used for the accurate definition of complex geometries with few parameters.…
A Nitche's method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented. In a non-conforming for- mulation,…
This paper introduces a watertight technique to deal with the boundary representation of surface-surface intersection in CAD. Surfaces play an important role in today's geometric design. The mathematical model of non-uniform rational…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
Second order spiral splines are $C^2$ unit-speed planar curves that can be used to interpolate a list $Y$ of $n+1$ points in $\R ^2$ at times specified in some list $T$, where $n\geq 2$. Asymptotic methods are used to develop a fast…
The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our…
Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…
We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given.…
In this paper, we present a novel algorithm that integrates deep learning with the polycube method (DL-Polycube) to generate high-quality hexahedral (hex) meshes, which are then used to construct volumetric splines for isogeometric…
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of…
The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct…
In this paper, we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of problems arising in electromagnetics and…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares…