I am looking to numerically solve many different integrals where the integrand is simply the indicator function for a region (i.e. 1 on the region, 0 outside. This is for measuring areas). The dimensions range from 1 to 5. What is an efficient quadrature method solving this? It seems like the standard methods which utilize polynomial approximations and derivatives wouldn't help in this case because the function is constant (and then discontinuous). You can think of the problem as having a simple integrand, but a complex region (with a continuous maybe even smoother boundary).Do you think that adaptive Monte Carlo methods like VEGAS or MISER integration will help out? Or is it just best to take a fine grid, sum up the function values at the grid points, and multiply by a constant (area of grid / number of points)?
Efficient Quadrature Methods for Indicator Functions?
numerical analysis;quadrature;monte carlo