How Long to Read Ray-based Finite Element Method for High-frequency Helmholtz Equations

How Long Does it Take to Read Ray-based Finite Element Method for High-frequency Helmholtz Equations?

It takes the average reader 1 hour and 42 minutes to read Ray-based Finite Element Method for High-frequency Helmholtz Equations by Jun Fang

Assuming a reading speed of 250 words per minute. Learn more

Description

In this dissertation we propose a ray-based finite element method (ray-FEM) for the high-frequency Helmholtz equation in smooth media, whose basis are learned adaptively from the medium and source. The method requires a fixed number of grid points per wavelength to represent the wave field; moreover, it achieves an asymptotic convergence rate of O(o-1/2), where o is the frequency parameter in the Helmholtz equation.The local basis are motivated by the geometric optics ansatz and are composed of polynomials modulated by plane waves propagating in a few dominant ray directions. The ray directions are learned by processing a low-frequency wave field that probes the medium with the same source. Once the local ray directions are extracted, they are incorporated into the local basis to solve the high-frequency Helmholtz equation. This process can be continued to further improve the approximations for both local ray directions and high-frequency wave fields iteratively.In addition, a fast sweeping-type preconditioner is used to solve the resulting linear system. We present numerical examples in 2D to show both efficiency and convergence of our method as the frequency becomes larger and larger. In particular, we show empirically that the overall complexity is O(o2) up to a poly-logarithmic factor.

How long is Ray-based Finite Element Method for High-frequency Helmholtz Equations?

Ray-based Finite Element Method for High-frequency Helmholtz Equations by Jun Fang is 102 pages long, and a total of 25,704 words.

This makes it 34% the length of the average book. It also has 31% more words than the average book.

How Long Does it Take to Read Ray-based Finite Element Method for High-frequency Helmholtz Equations Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 20 minutes to read Ray-based Finite Element Method for High-frequency Helmholtz Equations aloud.

What Reading Level is Ray-based Finite Element Method for High-frequency Helmholtz Equations?

Ray-based Finite Element Method for High-frequency Helmholtz Equations is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Ray-based Finite Element Method for High-frequency Helmholtz Equations?

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