A spectral solver for evolution problems with spatial S3-topology
نویسنده
چکیده
We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3spheres. Besides the main ideas, we discuss issues related to our implementation and analyze numerical test applications. Our main interest lies in cosmological solutions of Einstein’s field equations. Motivated by this, we also elaborate on problems of our approach for general tensorial evolution equations when certain symmetries are assumed. We restrict to U(1)and Gowdy symmetry here.
منابع مشابه
On two problems concerning the Zariski topology of modules
Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...
متن کاملA Differential Evolution and Spatial Distribution based Local Search for Training Fuzzy Wavelet Neural Network
Abstract Many parameter-tuning algorithms have been proposed for training Fuzzy Wavelet Neural Networks (FWNNs). Absence of appropriate structure, convergence to local optima and low speed in learning algorithms are deficiencies of FWNNs in previous studies. In this paper, a Memetic Algorithm (MA) is introduced to train FWNN for addressing aforementioned learning lacks. Differential Evolution...
متن کاملThe Power Spectrum, Bias Evolution, and the Spatial Three-Point Correlation Function
We calculate perturbatively the normalized spatial skewness, S3, and full three-point correlation function (3PCF), ζ , induced by gravitational instability of Gaussian primordial fluctuations for a biased tracer-mass distribution in flat and open cold-dark-matter (CDM) models. We take into account the explicit dependence on cosmological parameters, the shape and evolution of the CDM power spect...
متن کاملA numerical approach for hyperbolic problems with spatial S3-topology
We introduce a numerical method in order to compute solutions of hyperbolic partial differential equations on spatial domains diffeomorphic to S. We focus on the discussion of the mathematical background, our implementation and certain tests. Applications are analyzed elsewhere. We argue that this collocation approach has a wide applicability. In order to keep the discussion as transparent as p...
متن کاملA NEW MEMETIC SWARM OPTIMIZATION FOR SPECTRAL LAYOUT DESIGN OF BRACED FRAMES
For most practical purposes, true topology optimization of a braced frame should be synchronized with its sizing. An integrated layout optimization is formulated here to simultaneously account for both member sizing and bracings’ topology in such a problem. Code-specific seismic design spectrum is applied to unify the earthquake excitation. The problem is solved for minimal structural weight un...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comput. Physics
دوره 228 شماره
صفحات -
تاریخ انتشار 2009