SYLLABUS Previous: 1.4.7 Sampling with quasiparticles
Up: 1 INTRODUCTION
Next: 1.6 Exercises
1.5 Computer quiz
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 The equation
with
,
 is an ODE that can be solved for example with the RungeKutta method
 is an ODE that can only be solved only with an extra condition f(1)=0
 is a third order PDE that cannot be solved with a RungeKutta method
 The equation
has
 2 characteristics, i.e. solutions that propagate like waves
 1 characteristics, i.e. solutions that propagate like heat pulses
 0 characteristics, i.e. solutions that do no propagate
 When a heat pulse hits the edge of a perfectly insulated domain
 it leaves the domain while satisfying the Neuman boundary conditions
 it stops and reaches kind of a steady state
 it gets reflected and propagates backward inside the domain
 Advection/diffusion are not uniquely defined in an inhomogeneous
medium
 true: a diffusion coefficient gradient has the same effect as an advection
 false: advection and diffusion are always uniquely defined
 Successive doubling of the numerical resolution yields values
1.03, 2.98, 4.01, 4.50 that
 converge like the squareroot to a value around 6
 converge linearly to a value around 5
 converge quadratically to a value around 5
 do not seem to converge
 To approximate a Gaussian
with 1% accuracy
you need
 approx 100 linear FEM
 approx 1000 linear FEM
 approx 100 particles
 approx 10000 particles
SYLLABUS Previous: 1.4.7 Sampling with quasiparticles
Up: 1 INTRODUCTION
Next: 1.6 Exercises
