By Georg Radow
By Kinsuk Giri
By Laura F. Landweber,Erik Winfree
By Zohar Yosibash
This introductory and self-contained publication gathers as a lot particular mathematical effects at the linear-elastic and heat-conduction solutions in the community of singular issues in two-dimensional domain names, and singular edges and vertices in third-dimensional domain names. those are provided in an engineering terminology for sensible utilization. the writer treats the mathematical formulations from an engineering point of view and provides high-order finite-element methods for the computation of singular options in isotropic and anisotropic fabrics, and multi-material interfaces. The right interpretation of the implications in engineering perform is encouraged, in order that the computed information might be correlated to experimental observations.
The booklet is split into fourteen chapters, every one containing a number of sections.
Most of it (the first 9 Chapters) addresses two-dimensional domain names, where
only singular issues exist. the answer in a neighborhood of those issues admits an asymptotic growth composed of eigenpairs and associated generalized flux/stress depth components (GFIFs/GSIFs), that are being computed analytically whilst attainable or by means of finite point tools differently. Singular issues linked to weakly coupled thermoelasticity within the neighborhood of singularities also are addressed and thermal GSIFs are computed. The computed facts is critical in engineering perform for predicting failure initiation in brittle material every day. Several failure laws for two-dimensional domain names with V-notches are presented and their validity is tested by way of comparability to experimental observations. A enough easy and trustworthy for predicting failure initiation (crack formation) in micron point digital units, regarding singular points, remains to be a subject matter of energetic examine and curiosity, and is addressed herein.
Explicit singular recommendations within the neighborhood of vertices and edges in three-d domain names are supplied within the last 5 chapters. New tools for the computation of generalized part flux/stress depth services alongside singular edges are awarded and established by means of numerous instance difficulties from the sphere of fracture mechanics; together with anisotropic domain names and bimaterial interfaces. round edges also are offered and the writer concludes with a few comments on open questions.
This good illustrated publication will entice either utilized mathematicians and engineers operating within the box of fracture mechanics and singularities.
By Franco Brezzi,Piero Colli Franzone,Ugo Pietro Gianazza,Gianni Gilardi
By Leonard J. Kazmier
By Jonathan Tullis
By Dmitry V. Chalikov
By Themistocles M. Rassias,Vijay Gupta
By Heinz H. Bauschke,Regina Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz
"Fixed-Point Algorithms for Inverse difficulties in technological know-how and Engineering" offers a few of the newest paintings from top-notch researchers learning projection and different first-order fixed-point algorithms in numerous components of arithmetic and the technologies. the fabric offered offers a survey of the state of the art idea and perform in fixed-point algorithms, deciding upon rising difficulties pushed by means of functions, and discussing new techniques for fixing those problems.
This ebook accommodates assorted views from broad-ranging components of study together with, variational research, numerical linear algebra, biotechnology, fabrics technology, computational solid-state physics, and chemistry.
Topics awarded include:
idea of Fixed-point algorithms: convex research, convex optimization, subdifferential calculus, nonsmooth research, proximal element tools, projection tools, resolvent and similar fixed-point theoretic equipment, and monotone operator theory.
Numerical research of fixed-point algorithms: number of step lengths, of weights, of blocks for block-iterative and parallel tools, and of leisure parameters; regularization of ill-posed difficulties; numerical comparability of varied methods.
parts of functions: engineering (image and sign reconstruction and decompression problems), computing device tomography and radiation therapy making plans (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular constitution reconstruction), computational chemistry (molecular constitution simulation) and different areas.
Because of the diversity of purposes offered, this booklet can simply function a foundation for brand spanking new and innovated learn and collaboration.