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# lump

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# lump   { LUMP.PDE

This example illustrates use of the LUMP function.

LUMP(F) saves an averaged value of F in each mesh cell, and returns the same

value for any position within the cell.

Notice that LUMP(F) is NOT the same as the "lumped parameters" frequently referred to

in finite element literature.

LUMP(f) is syntactically like SAVE(f), in that it stores a representation of

its argument for later use.

}

title 'LUMP test'

select

contourgrid=400 { use a very dense plot grid to show lump structure }

Variables

u

definitions

k = 2

u0 = 1+x^2+y^2

s = u0 - 4*k

lumps = lump(s)       { Used in a definition }

Initial values

u = 1

equations

U: u - div(K*grad(u))  = s

boundaries

Region 1

start(-1,-1)

value(u)=u0

line to (1,-1) to (1,1) to (-1,1) to close

monitors

contour(u)

plots

grid(x,y)

contour(u)

contour(s)

contour(lump(s))   as "Lumped Source - Direct Reference"

contour(lumps) as "Lumped Source - Defined Parameter"

end