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1.5 Computer quiz

  1. Do you have to register to study this course on-line?
    1. all the material can be accessed free of charge
    2. register to gain access to restricted material and pedagogical support
    3. all the services on this website are for members only

  2. The equation $ \partial_{xxx}f -\partial_{xx}f\sqrt{1+(\partial_x f)^2}=\sin(xf)$ with $ f(0)=0$ , $ f^\prime(0)=1$
    1. is an ODE that can be solved for example with the Runge-Kutta method
    2. is an ODE that can only be solved only with an extra condition f(1)=0
    3. is a third order PDE that cannot be solved with a Runge-Kutta method

  3. The equation $ 2\partial_{tt}f -2\partial_{xt}f +2\partial_{xx}f=0$ has
    1. 2 characteristics, i.e. solutions that propagate like waves
    2. 1 characteristics, i.e. solutions that propagate like heat pulses
    3. 0 characteristics, i.e. solutions that do no propagate

  4. When a heat pulse hits the edge of a perfectly insulated domain
    1. it leaves the domain while satisfying the Neuman boundary conditions
    2. it stops and reaches kind of a steady state
    3. it gets reflected and propagates backward inside the domain

  5. Advection/diffusion are not uniquely defined in an inhomogeneous medium $ D=D(x)$
    1. true: a diffusion coefficient gradient has the same effect as an advection
    2. false: advection and diffusion are always uniquely defined

  6. Successive doubling of the numerical resolution yields values 1.03, 2.98, 4.01, 4.50 that
    1. converge like the square-root to a value around 6
    2. converge linearly to a value around 5
    3. converge quadratically to a value around 5
    4. do not seem to converge

  7. To approximate a Gaussian $ \exp(-x^2), x\in[-3; 3]$ with 1% accuracy you need
    1. approx 100 linear FEM
    2. approx 1000 linear FEM
    3. approx 100 particles
    4. approx 10000 particles

SYLLABUS  Previous: 1.4.7 Sampling with quasi-particles  Up: 1 INTRODUCTION  Next: 1.6 Exercises

      
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