Abstract: Harmonic functions are solutions to Laplace’s equation
that are known to have an advantage as a global approach in providing
the potential values for autonomous vehicle navigation. However,
the computation for obtaining harmonic functions is often too slow
particularly when it involves very large environment. This paper
presents a two-stage iterative method namely Modified Arithmetic
Mean (MAM) method for solving 2D Laplace’s equation. Once
the harmonic functions are obtained, the standard Gradient Descent
Search (GDS) is performed for path finding of an autonomous vehicle
from arbitrary initial position to the specified goal position. Details
of the MAM method are discussed. Several simulations of vehicle
navigation with path planning in a static known indoor environment
were conducted to verify the efficiency of the MAM method. The
generated paths obtained from the simulations are presented. The
performance of the MAM method in computing harmonic functions
in 2D environment to solve path planning problem for an autonomous
vehicle navigation is also provided.
Abstract: In this paper, the velocity potential and stream
function of capture zone for a well field in an aquifer bounded by two
parallel streams with or without a uniform regional flow of any
directions are presented. The well field includes any number of
extraction or injection wells or a combination of both types with any
pumping rates. To delineate the capture envelope, the potential and
streamlines equations are derived by conformal mapping method.
This method can help us to release constrains of other methods. The
equations can be applied as useful tools to design in-situ groundwater
remediation systems, to evaluate the surface–subsurface water
interaction and to manage the water resources.