mjhjmtu

I need to draw a contour figure defined by coordinate x and y. The domain is a rectangle (-100<=x<=100,-100<=y<=100) excluding a circle (center at the origin, and radius of 5). The object function is 'z=x+y'.

What confuses me is how to exclude the circle from the rectangle. How can I draw such a contour figure?

You can also use ConditionalExpression as the first argument of ContourPlot:

ContourPlot[ConditionalExpression[x + y, x^2 + y^2 >= 5^2],
 x, -100, 100, y, -100, 100, PlotLegends -> Automatic]

How about this?

ContourPlot[x + y, x, -100, 100, y, -100, 100, 
 RegionFunction -> Function[x, y, z, x^2 + y^2 >= 5^2], 
 PlotPoints -> 100, PerformanceGoal -> "Quality", 
 PlotLegends -> Automatic, ColorFunction -> "ThermometerColors"]

If the smoothness of disk bothers you (it bothers me), you can cheat it like so:

Show[ContourPlot[x + y, x, -100, 100, y, -100, 100, 
 PlotPoints -> 100, PerformanceGoal -> "Quality", 
 PlotLegends -> Automatic, ColorFunction -> "ThermometerColors"], 
 Graphics[White, Disk[0, 0, 5]]]