大质量比双黑洞给数值相对论带来的挑战

1、 zhoujian caoinstitute of applied mathematics, amss 2013-10-23workshop on collapsing objects, fudan universitygeneralized bondi-sachs equations for numerical relativityoutline features of numerical relativity code amss-ncku motivation for generalized bondi-sachs equations generalized bondi-sachs equ

2、ations for numerical relativity summarynr code amss-ncku developers include: shan bai (amss), zhoujian cao (amss), zhihui du (thu), chun-yu lin (ncku), quan yang (thu), hwei-jang yo (ncku), jui-ping yu (ncku) 2007-now2+2: characteristic formulationcharacteristic formulationformulations implemented b

3、ssnok shibata and nakamura prd 52, 5428 (1995), baumgarte and shapiro prd 59, 024007 (1998) z4c bernuzzi and hilditch prd 81, 084003 (2010), cao and hilditch prd 85, 124032 (2012) modified bssn yo, lin and cao prd 86, 064027(2012) bondi-sachs cao ijmpd 22, 1350042 (2013)mesh refinementmesh refinemen

4、tparallel structured mesh refinement (psamr), co work with brandt, du and loffler, 2013mesh refinementhilditch, bernuzzi, thierfelder, cao, tichy and brugeman (2012)code structurempi + openmp + cudaoutline features of numerical relativity code amss-ncku motivation for generalized bondi-sachs equatio

5、ns generalized bondi-sachs equations for numerical relativity summarybbh models for gw detectioncomparison between our result and calibrated eob modeltcowork with yi pan (2012)bbh models for gw detection?last problem for bbh modelsimulation efficiency (speed): psamr gpu implicit method lau, lovelace

6、 and pfeiffer prd 84, 084023 cauchy characteristic matching winicour living rev. relativity 15 (2012)last problem for bbh modelsimulation efficiency: psamr gpu implicit method lau, lovelace and pfeiffer prd 84, 084023 cauchy characteristic matching winicour living rev. relativity 15 (2012)1. touch n

7、ull infinity without extra computational cost 2. save propagation timet for cauchyt for characauchy-characteristic matching (ccm) many works have been contributed to ccm pittsburgh, southampton 1990s but hard to combine! difficulty 1. different evolution scheme difficulty 2. different gauge conditio

8、nexisting characteristic formalisms null quasi-spherical formalisms2 of constant u and r should admit standard spherical metricexisting characteristic formalisms southampton bondi-sachs formalismexisting characteristic formalisms pittsburgh bondi-sachs formalismrelax the form requirement, but essent

9、ially r is the luminosity distance parameterexisting characteristic formalisms affine bondi-sachs formalismin contrast to luminosity parameter, affine parameter can be matched to any single layer of coordinate cylinder routline features of numerical relativity code amss-ncku motivation for generaliz

10、ed bondi-sachs equations generalized bondi-sachs equations for numerical relativity summarygeneralized bondi-sachs formalismrequirements:1. is null2. is hypersurface forming in contrast to the existing bondi-sachs formalism, the parameterization of r is totally freea,b = 2,3 guarantees that we can u

11、se main equations only to do free evolutiongeneralized bondi-sachs equations in order to be a characteristic formalism, we need nested ode structure, fortunately we have!generalized bondi-sachs equationsthere is no term involved, so for given , its ode generalized bondi-sachs equationsgeneralized bo

12、ndi-sachs equationsthere is no term involved, its second order ode systemi,j = 1,2,3generalized bondi-sachs equationsgeneralized bondi-sachs equationsthere is no term involved, its ode systemgiven on get get get update to cowork with xiaokai he (2013)given on update to 1. nested ode structure2. faci

13、litate us to use mol which makes us to evolve cauchy part and characteristic part with the same numerical scheme cao, ijmpd 22, 135042 (2013)gauge variable 1.there is no equation to control2. is related to parameterization of r is a gauge freedom, it is possible to use this freedom to relate the gauge used in inner cauchy part for ccmpossible application of gbs to ccmcauchy characteristic cartesian spherical design equation to control by try and errorsummary feature of amss-ncku code efficiency problem in bbh model ccm can improve efficiency, b