A Survey of the m-M Calculus
A survey on wavelet methods for (geo) applications.
Wavelets originated in 1980's for the analysis of (seismic) signals and have seen an explosion of applications. However, almost all the material is based on wavelets over Euclidean spaces. This paper deals with an approach to the theory and algorithmic aspects of wavelets in a general separable Hilbert space framework. As examples Legendre wavelets on the interval [-1,+1] and scalar and vector spherical wavelets on the unit sphere 'Omega' are discussed in more detail.
Algoritmy na výpočet kořenů polynomu
Diffpack technical summary
Euclid΄s algorithm and accelerated iterative methods
Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists
Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order...
From classical numerical mathematics to scientific computing.
Geometry processing : intersections, contours, and cubatures
Il problema della stabilità per metodi numerici per ODEs
Local accuracy in finite element analysis using curved isoparametric elements
The finite element method (FEM) is popularly used for numerically approximating PDE(s) over complicated domains due to its rich mathematical background, versatility, and ease of implementation. In this article, we investigate one of its important features, i.e., the approximation of PDE(s) over nonpolygonal Lipschitz domains by higher-order simplicial elements in 2D and 3D. This important issue is not well understood and often ignored by engineers due to its mathematical complexity, i.e., the FEM...
Numerical analysis and systems theory
The area of numerical analysis interacts with the area of control and systems theory in a number of ways, some of which are widely recognized and some of which are not fully appreciated or understood. This paper will briefly discuss some of these areas of interaction and place the papers in this volume in context.
Object oriented design philosophy for scientific computing
This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...
Object oriented design philosophy for scientific computing
This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...
Operator preconditioning with efficient applications for nonlinear elliptic problems
This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.
Rozděl a slep aneb jak řešit soustavu s bilionem lineárních rovnic
Cílem článku je naznačit úlohu matematiky a efektivnost nových algoritmů pro řešení rozsáhlých soustav lineárních rovnic na současných masívně paralelních superpočítačích. Na příkladu řešení Poissonovy rovnice je popsána základní varianta metody rozložení oblasti typu FETI (finite element tearing and interconnecting) s projektorem na přirozenou hrubou síť, jsou odvozeny základní kvalitativní výsledky demonstrující asymptoticky lineární (optimální) složitost řešení a jsou popsána prakticky důležitá...
Верхние оценки сложности решения систем линейных уравнений
Вычислительные методы линейной алгебры
Поправка к работе: Вычислительные методы линейной алгебры