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In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…
In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
The geometric state of a flat boundary is frequently described using the so-called macroscopic parameters. They are a principal tool for dealing with interfaces at the continuous scale. The paper describes a new method for macroscopic…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
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…
Computing the envelope of deforming planar domains is a significant and challenging problem with a wide range of potential applications. We approximate the envelope using circular arc splines, curves that balance geometric flexibility and…
The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the…
Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard…
Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is…
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…
In the error analysis of finite element methods, the shape regularity assumption on triangulations is typically imposed to obtain a priori error estimations. In practical computations, however, very thin or degenerated elements that violate…
A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…
A novel application of the Pade approximation is proposed in which the Pade approximant is used as an interpolation for the small and large coupling behaviors of a physical system, resulting in a prediction of the behavior of the system at…
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful…