If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.Įnter your library card number to sign in. Following successful sign in, you will be returned to Oxford Academic.Do not use an Oxford Academic personal account. When on the institution site, please use the credentials provided by your institution.Select your institution from the list provided, which will take you to your institution's website to sign in.Click Sign in through your institution.Shibboleth / Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.Ĭhoose this option to get remote access when outside your institution. Typically, access is provided across an institutional network to a range of IP addresses. If you are a member of an institution with an active account, you may be able to access content in one of the following ways: Get help with access Institutional accessĪccess to content on Oxford Academic is often provided through institutional subscriptions and purchases. Finally, we show how Filon methods with recursive moment computation can be applied to efficiently compute integrals arising in hybrid numerical-asymptotic collocation methods for high-frequency wave scattering on a screen. For the Hankel kernel, we derive error estimates that describe the convergence behaviour of the method in terms of frequency and number of Filon quadrature points. We provide rigorous stability results for the moment computation for the first of these classes and demonstrate how the corresponding Filon method results in an accurate approximation at truly frequency-independent cost. We discuss in further detail the application to two classes of particular interest: integrals with algebraic singularities and stationary points and integrals involving a Hankel function. In this work we demonstrate how recurrences can be constructed for a wide class of oscillatory kernel functions, based on the observation that many physically relevant kernel functions are in the null space of a linear differential operator whose action on the Filon interpolation basis is represented by a banded (infinite) matrix. A crucial step in the implementation of these methods is the accurate and fast computation of the Filon quadrature moments. We study the efficient approximation of highly oscillatory integrals using Filon methods.
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