Computational Fluid Dynamics Questions and Answers – Discretization Aspects – Thomas Algorithm

This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Discretization Aspects – Thomas Algorithm”.

1. Thomas algorithm is a ___________
a) Linear equations solver
b) Quadratic equations solver
c) Discretization method
d) Linear least square system
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2. Thomas algorithm can be used to solve __________
a) any matrix
b) all square matrices
c) only penta-diagonal matrices
d) only tri-diagonal matrices
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3. Thomas algorithm is _________
a) an analytical method
b) a direct method
c) an iterative method
d) a least squares method
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4. Consider a system of equations where the i^th equation is a_i Φ_i=b_i Φ_(i+1)+c_i Φ_(i+1)+d_i. While solving this system using Thomas algorithm, we get Φ_i=P_i Φ_(i+1)+Q_i. What are P_i and Q_i?
a) \(P_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}};Q_i=\frac{b_i}{a_i-c_i P_{i-1}}\)
b) \(P_i=\frac{b_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}}\)
c) \(P_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i=\frac{d_i}{a_i-c_i P_{i-1}}\)
d) \(P_i=\frac{d_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}}\)
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5. Let the i^th equation of a system of n equations be a_iΦ_i=b_i Φ_i+1+c_iΦ_i-1+d_i. Which of these is correct?
a) c_N=0; b_N=0
b) c_N=0; b₁=0
c) c₁=0; b_N=0
d) c₁=0; b₁=0
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6. Using the Thomas algorithm, if the i^th unknown is Φ_i=P_i Φ_i+1+Q_i. what is the last unknown value Φ_N equal to?
a) 0
b) P_N
c) Q_N
d) 1
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7. While solving a system of equations with the Thomas algorithm, in which order are the values of P_i and Q_i found?
a) Backwards
b) Forward
c) Simultaneously
d) Depends on the problem
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8. After finding all the values of P_i and Q_i, in which order are the values of Φ_i found?
a) Forward
b) Simultaneously
c) Backwards
d) Depends on the problem
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9. Consider a system of equations where the i^th equation is a_iΦ_i=b_i Φ_i+1+c_iΦ_i-1+d_i. While solving this system using Thomas algorithm, we get Φ_i=P_iΦ_i+1+Q_i. What are P₁ and Q₁?
a) \(P_1=\frac{d_1}{a_1-c_1};Q_1=\frac{b_1}{a_1-c_1}\)
b) \(P_1=\frac{b_1}{a_1-c_1};Q_1=\frac{d_1}{a_1-c_1}\)
c) \(P_1=\frac{d_1}{a_1};Q_1=\frac{b_1}{a_1}\)
d) \(P_1=\frac{b_1}{a_1};Q_1=\frac{d_1}{a_1}\)
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10. A system of equations with which of these coefficient matrices can be solved using the Thomas algorithm?
a) \(\begin{bmatrix}
1 & 2 & 0 \\
3 & 4 & 5 \\
0 & 6 &7
\end{bmatrix} \)
b) \(\begin{bmatrix}
1 & 2 & 3 \\
0 & 4 & 5 \\
0 & 0 & 7
\end{bmatrix}\)
c) \(\begin{bmatrix}
1 & 0 & 0 \\
3 & 4 & 0 \\
5 & 6 & 7
\end{bmatrix}\)
d) \(\begin{bmatrix}
1 & 2 & 3 \\
3 & 4 & 5 \\
5 & 6 & 7
\end{bmatrix}\)
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