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Test 1 - MATHEMATICAL AND NUMERICAL METHODS IN ENGINEERING - NUMERICAL PART Prof. P. Zunino Total duration of the exam 1h45min ! Ciao Chiara, quando invierai il modulo, il proprietario potrà vedere il tuo nome e l'indirizzo di posta elettronica. Part I Quiz Answer to the following questions: 1 The condition number of matrix A arising from finite difference discretization of the Poisson problem is given by: (1 punto) /u1D43E(/u1D434) /similar_equal /uni210E2 /u1D43E(/u1D434) /similar_equal/uni210E−2 /u1D43E(/u1D434)/similar_equal()∆/u1D461 /uni210E 2 /u1D43E(/u1D434)/similar_equal/uni210E−1 2 Which of the following is the Upwind scheme for a conservation law with convection given by β? (1 punto) =+2∆/u1D461 /u1D448/u1D45B+1 /u1D457/u1D448/u1D45B/u1D457 /u1D6FD /uni210E/u1D448/u1D45B /u1D457−1 =(1−∆/u1D461 )+/u1D448/u1D45B+1/u1D457 /u1D6FD /uni210E/u1D448/u1D45B/u1D457/u1D448/u1D45B /u1D457−1 =(1−∆/u1D461 ) + ∆/u1D461 /u1D448/u1D45B+1/u1D457 /u1D6FD /uni210E/u1D448/u1D45B/u1D457 /u1D6FD /uni210E/u1D448/u1D45B /u1D457−1 =(1−∆/u1D461 )(− )/u1D448/u1D45B+1/u1D457 /u1D6FD /uni210E/u1D448/u1D45B/u1D457/u1D448/u1D45B /u1D457−1 3 The meaning of CFL condition is that: (1 punto) The numerical solution propagates faster than the analytical one It allows to have a null error The numerical solution propagates slower than the analytical one The numerical solution propagates with the same velocity of the analytical one 4 The Backward Euler approximation of the heat equation in algebraic form is given by (A is the matrix related to the approximation of Poisson problem with +2 on the main diagonal and µ the diffusion parameter): (1 punto) (/u1D43C− /u1D434) =+∆/u1D461 /u1D707∆/u1D461 /uni210E2 /u1D448/u1D45B+1 /u1D448/u1D45B/u1D439/u1D45B+1 =(/u1D43C− /u1D434)+∆/u1D461 /u1D448/u1D45B+1…