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Numerical Methods For Partial Differential Equations
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Numerical methods for partial differential equations is available in the digital library an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.Abstract:
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Citations
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Journal ArticleDOI
TauFactor: An open-source application for calculating tortuosity factors from tomographic data
TL;DR: TauFactor is a MatLab application for efficiently calculating the tortuosity factor, as well as volume fractions, surface areas and triple phase boundary densities, from image based microstructural data, without requiring high computational power.
Journal ArticleDOI
Weak adversarial networks for high-dimensional partial differential equations
TL;DR: This paper converts the problem of finding the weak solution of PDEs into an operator norm minimization problem induced from the weak formulation, and parameterized as the primal and adversarial networks respectively, which are alternately updated to approximate the optimal network parameter setting.
Journal ArticleDOI
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations
TL;DR: The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined deep learning, revolutionized the area of deep learning.
Posted Content
Rateless Codes for Near-Perfect Load Balancing in Distributed Matrix-Vector Multiplication
TL;DR: This paper proposes a rateless fountain coding strategy that achieves the best of both worlds -- it is proved that its latency is asymptotically equal to ideal load balancing, and it performs asymPTotically zero redundant computations.
Journal ArticleDOI
An Intelligent Decision Support System for Leukaemia Diagnosis using Microscopic Blood Images.
Siew Chin Neoh,Worawut Srisukkham,Li Zhang,Stephen Todryk,Brigit Greystoke,Chee Peng Lim,Mohammed Alamgir Hossain,Nauman Aslam +7 more
TL;DR: A novel clustering algorithm with stimulating discriminant measures (SDM) of both within- and between-cluster scatter variances is proposed to produce robust segmentation of nucleus and cytoplasm of lymphocytes/lymphoblasts for acute lymphoblastic leukaemia diagnosis from microscopic blood images.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Finite Element Method for Elliptic Problems
TL;DR: In this article, Ciarlet presents a self-contained book on finite element methods for analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces.
Book
The Mathematical Theory of Finite Element Methods
TL;DR: In this article, the construction of a finite element of space in Sobolev spaces has been studied in the context of operator-interpolation theory in n-dimensional variational problems.
Book
Elliptic Problems in Nonsmooth Domains
TL;DR: Second-order boundary value problems in polygons have been studied in this article for convex domains, where the second order boundary value problem can be solved in the Sobolev spaces of Holder functions.
Book
Numerical Approximation of Partial Differential Equations
Alfio Quarteroni,Alberto Valli +1 more
TL;DR: In this article, the authors provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation.