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Full-Text Articles in Physical Sciences and Mathematics
Testing The Well-Posedness Of Characteristic Evolution Of Scalar Waves, Maria Babiuc-Hamilton, Heinz Otto Kreiss, Jeffrey Winicour
Testing The Well-Posedness Of Characteristic Evolution Of Scalar Waves, Maria Babiuc-Hamilton, Heinz Otto Kreiss, Jeffrey Winicour
Maria C. Babiuc-Hamilton
Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for scalar waves well posed even on a background spacetime with closed lightlike curves. These results provide new guidance for developing stable characteristic evolution algorithms. In this regard, we present here the finite difference version of these recent results and implement them in a stable evolution code. We describe test results which validate the code and exhibit some of the interesting features due …
Strategies For The Characteristic Extraction Of Gravitational Waveforms, Maria C. Babiuc-Hamilton, N. T. Bishop, B´Ela Szila´Gyi, Jeffrey Winicour
Strategies For The Characteristic Extraction Of Gravitational Waveforms, Maria C. Babiuc-Hamilton, N. T. Bishop, B´Ela Szila´Gyi, Jeffrey Winicour
Maria C. Babiuc-Hamilton
We develop, test, and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component Ψ4 to extract the waveform as opposed to the …
Characteristic Extraction Tool For Gravitational Waveforms, Maria C. Babiuc-Hamilton, B´Ela Szila´Gyi, Jeffrey Winicour, Yosef Zlochower
Characteristic Extraction Tool For Gravitational Waveforms, Maria C. Babiuc-Hamilton, B´Ela Szila´Gyi, Jeffrey Winicour, Yosef Zlochower
Maria C. Babiuc-Hamilton
We develop and calibrate a characteristic waveform extraction tool whose major improvements and corrections of prior versions allow satisfaction of the accuracy standards required for advanced LIGO data analysis. The extraction tool uses a characteristic evolution code to propagate numerical data on an inner worldtube supplied by a 3+1 Cauchy evolution to obtain the gravitational waveform at null infinity. With the new extraction tool, high accuracy and convergence of the numerical error can be demonstrated for an inspiral and merger of mass M binary black holes even for an extraction worldtube radius as small as R=20M. The tool provides a …