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ea06fd8cde
This was a seperate repository in CVS and so it missed the conversion.
benchmarks/
As above.
98 lines
3.6 KiB
Haskell
98 lines
3.6 KiB
Haskell
--
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-- Patricia Fasel
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-- Los Alamos National Laboratory
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-- 1990 August
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--
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-- Copyright, 1990, The Regents of the University of California.
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-- This software was produced under a U.S. Government contract (W-7405-ENG-36)
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-- by the Los Alamos National Laboratory, which is operated by the University
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-- of California for the U.S. Department of Energy. The U.S. Government is
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-- licensed to use, reproduce, and distribute this software. Permission is
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-- granted to the public to copy and use this software without charge, provided
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-- that this notice and any statement of authorship are reproduced on all
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-- copies. Neither the Government nor the University makes any warranty,
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-- express or implied, or assumes any liability for the use of this software.
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module Pic (pic) where
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import PicType
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import Consts
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import Utils
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import ChargeDensity
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import Potential
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import ElecField
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import PushParticle
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import Data.Array
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-- PIC, particle in cell, a basic electrodynamics application
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-- Given an initial configuration of particles, follow how they move under the
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-- electric field they induce
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-- Torroidal boundary conditions are assumed, so wrap in both dimensions
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-- given nPart the number of particles considered
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-- given nStep the number of time steps to put the particles through
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-- given nCell the dimension of the matrix of cells
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pic :: Indx -> [Char]
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pic nPart =
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show dt'
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where
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partHeap = initParticles nPart
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dt = 0.001
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phi = initPhi partHeap
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(dt', phi', partHeap') = timeStep partHeap phi dt 0 nStep
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-- during each time step perform the following calculations
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-- calculate the charge density (rho), using position of particles
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-- calculate the new potential (phi), by solving Laplace's equation
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-- del2(phi) = rho , using rho and phi of last timestep
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-- calculate the electric field, E = del(phi), using phi of this time step
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-- push each particle some distance and velocity using electric field, for a
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-- timestep deltaTime, small enough that no particle moves more than the
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-- width of a cell
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-- an NxN mesh is used to represent value of x and y in the interval [0,1]
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-- so delta_x = delta_y = 1/n
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--
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-- phi ((0,0), (n,n)) = electrostatic potential at grid point (i,j)
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-- rho ((0,0), (n,n)) = charge density at grid point (i,j)
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-- xElec ((0,0), (n,n)) = x component of electric field between (i,j) (i,j+1)
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-- yElec ((0,0), (n,n)) = y component of electric field between (i,j) (i+1,j)
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-- [xyPos] = (x,y) coordinate of particle displacement in units of delta_x
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-- [xyVel] = (x,y) coordinate of particle velocity in units of delta_x/sec
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timeStep :: ParticleHeap -> Phi -> Value -> Indx -> Indx -> (Value, Phi, ParticleHeap)
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timeStep partHeap phi dt depth step
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| step == 0 = (dt, phi, partHeap)
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| otherwise =
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timeStep partHeap' phi' dt' depth' (step-1)
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where
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rho = chargeDensity partHeap
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phi' = potential phi rho depth 1
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xyElec = elecField phi'
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(maxVel, maxAcc, partHeap') =pushParticle partHeap xyElec dt 0 0
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dt' = (sqrt (maxVel*maxVel + 2*maxAcc) - maxVel) / maxAcc
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depth' = (depth+1) `rem` maxDepth
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initParticles :: Indx -> ParticleHeap
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initParticles nPart =
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(xyPos, xyVel)
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where
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nCellD = fromIntegral nCell
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nPartD = fromIntegral (nPart+1)
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xyPos = [(xPos,yPos) |
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i <- [1..nPart],
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xPos <- [nCellD * genRand (fromIntegral i/ nPartD)],
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yPos <- [nCellD * genRand xPos]]
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xyVel = [(0.0,0.0) | i <- [1..nPart]]
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initPhi :: ParticleHeap -> Phi
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initPhi partHeap =
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potential phi0 rho maxDepth 1
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where
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rho = chargeDensity partHeap
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phi0 = array ((0,0), (n,n))
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[((i,j), 0.0) | i <- [0..n], j <- [0..n]]
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n = nCell-1
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