Publication

Efficient computation of Sommerfeld integral tails - methods and algorithms

Juan Ramon Mosig, Krzysztof Michalski
2016
Reviews

Abstract

A review is presented of the most effective methods for the computation of Sommerfeld integral tails. Such integrals, which are often oscillatory, singular and divergent, commonly arise in layered media Green functions. The mathematical foundations of various pertinent methods are discussed in detail and their performance is illustrated by relevant numerical examples. The associated algorithms are given in pseudocode for their easy computer implementation.

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https://infoscience.epfl.ch/entities/publication/c787e5fc-294d-4b3b-a2b1-a53ce0a16427

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Juan Ramon Mosig, Krzysztof Michalski
2016
Reviews

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/c787e5fc-294d-4b3b-a2b1-a53ce0a16427

About this result

Related concepts (13)

New Foundations

In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name. Much of this entry discusses NF with urelements (NFU), an important variant of NF due to Jensen and clarified by Holmes. In 1940 and in a revision in 1951, Quine introduced an extension of NF sometimes called "Mathematical Logic" or "ML", that included proper classes as well as sets.

Mathematical logic

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.

Foundations of mathematics

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.

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