Quasi Monte Carlo method gives zero for the following example

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Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration







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    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago














up vote
2
down vote

favorite












Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration







share|improve this question

















  • 1




    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago












up vote
2
down vote

favorite









up vote
2
down vote

favorite











Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration







share|improve this question













Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration




numerical-integration






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asked 4 hours ago









John Taylor

600211




600211







  • 1




    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago












  • 1




    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago







1




1




The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
– Henrik Schumacher
4 hours ago




The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
– Henrik Schumacher
4 hours ago










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xmax = ymax = 1000;
NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
 Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



7.06875







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    up vote
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    accepted










    xmax = ymax = 1000;
    NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
     Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



    7.06875







    share|improve this answer
























      up vote
      3
      down vote



      accepted










      xmax = ymax = 1000;
      NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
       Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



      7.06875







      share|improve this answer






















        up vote
        3
        down vote



        accepted







        up vote
        3
        down vote



        accepted






        xmax = ymax = 1000;
        NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
         Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



        7.06875







        share|improve this answer












        xmax = ymax = 1000;
        NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
         Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



        7.06875








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        share|improve this answer










        answered 4 hours ago









        kglr

        163k8188387




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