This is the outline of the main idea behind
the numerical integration method over the meshfree geometric
domain (Figure 1) to be described in details
in the forthcoming publications:
hierarchically decompose the domain using
quadtree/octree technique (Figure 2);
analyze the intersection of the cells with
the domain (Figure 3);
allocate the integration knots inside the
cell accordingly with the type of its intersection
with the domain (Figure 4);
perform the integration over the domain
evaluating the function at the allocated integration knots
(Figure 5).
Figure 1: A geometric domain for integration
Figure 2: A hierarchical space decomposition
Figure 3: The classification of the intersection types of the
rectangular cells with domain
Figure 4: Allocation of the integration knots depends on the
type of the intersection
