First and Last Passage Random Walk Algorithms.
Michael Mascagni
Department of Computer Science, Florida State University
Monday, December 10, 2001 15:00-16:00,
Room 145, NIST North (820)
Gaithersburg
Monday, December 10, 2001 13:00-14:00,
Room 4511
Boulder
Abstract:
We present two complimentary Monte Carlo methods for
computing the charge density on a
conductor when that conductor is at potential
V0 with respect to
infinity.The first method extends our previous first-passage algorithm for
calculating the capacitance of an arbitrarily shaped conducting object.
The capacitance of an object can be probabilistically calculated finding the
probability that a Brownian walker starting at infinity hits the region before
returning to infinity. It is a standard result from probabilistic
potential theory that the absorption locations of the first-passage capacitance calculation give
the charge distribution on the conducting object. The second Monte Carlo method utilizes the last-passage
concept. This last-passage method stems from the consideration of the
isomorphism between the electrostatic potential and the probability of going to
infinity without touching a conducting object at a certain distance from the
conductor. This is analogous to `adjoint' methods, where
time-reversedwalks are used to solve the adjoint problem.
We demonstrate our methods
for computing an analytically known charge
density on a two dimensional thin disk in three dimensions.
In addition we solve for the charge distribution on the unit
cube using an edge distribution concept. Computing the capacitance of the
unit cube is considered the most important open problem in electrostatics, and
we not only have the most accurate calculation, but the edge distribution
computation provides results never before computed.
Contact: R. F. BoisvertNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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