MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Computational Fluid Dynamics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
In incomplete Cholesky decomposition, the preconditioner matrix produced is ____________ (Note: L is the factorized lower triangular matrix and U is the factorized lower triangular matrix). |
| A. | UL’ |
| B. | LU’ |
| C. | LL’ |
| D. | LL2 |
| Answer» D. LL2 | |
| 2. |
Which of these methods is not restricted to symmetric positive definite matrices? |
| A. | The method of steepest descent |
| B. | Conjugate gradient method |
| C. | Bi-conjugate gradient method |
| D. | Gauss-Seidel method |
| Answer» E. | |
| 3. |
In which of these methods, after factorization, the pattern of zero elements in the combined L and U matrices the same as the original coefficient matrix? |
| A. | LU decomposition |
| B. | ILU decomposition |
| C. | ILU(0) decomposition |
| D. | ILU(1) decomposition |
| Answer» B. ILU decomposition | |
| 4. |
What does the letter ‘I’ stand for in ILU decomposition problem? |
| A. | Inbuilt |
| B. | Incomplete |
| C. | Iterative |
| D. | Imbalanced |
| Answer» C. Iterative | |
| 5. |
Preconditioners improve ____________ of the coefficient matrix. |
| A. | sparsity |
| B. | rank |
| C. | spectral properties |
| D. | Singularity |
| Answer» D. Singularity | |
| 6. |
When compared to the Jacobi method, the Gauss-Siedel method ____________ |
| A. | has better convergence and needs less memory |
| B. | has less convergence and needs more memory |
| C. | has less convergence and needs less memory |
| D. | has better convergence and needs more memory |
| Answer» B. has less convergence and needs more memory | |
| 7. |
Consider the global matrix AΦ=b. What is the residual at the ith iteration? (Note: Φi is the value of Φ in the ith iteration). |
| A. | AΦi-1+b |
| B. | AΦi-1-b |
| C. | AΦi+b |
| D. | AΦi-b |
| Answer» E. | |
| 8. |
Consider the global matrix AΦ=b. Let the coefficient matrix A=M-N. At the ith iteration, the general form can be given as ______________ (Note: Φi is the value of Φ in the ith iteration). |
| A. | MΦi=NΦi-1+b |
| B. | MΦi=NΦi+b |
| C. | MΦi=NΦi-1-b |
| D. | MΦi=NΦi-b |
| Answer» B. MΦi=NΦi+b | |
| 9. |
Let us divide the coefficient matrix into this form: A=D+L+U. Which of these matrices can be L in this equation? |
| A. | \(\begin{bmatrix}1 & 0 & 0 \\2 & 1 & 0 \\3 & 4 & 1\end{bmatrix}\) |
| B. | \(\begin{bmatrix}0 & 0 & 0 \\2 & 0 & 0 \\3 & 4 & 0\end{bmatrix}\) |
| C. | \(\begin{bmatrix}1 & 0 & 0 \\2 & 5 & 0 \\3 & 4 & 6\end{bmatrix}\) |
| D. | \(\begin{bmatrix}1 & 0 & 0 \\0 & 2 & 0 \\0 & 0 & 3\end{bmatrix}\) |
| Answer» C. \(\begin{bmatrix}1 & 0 & 0 \\2 & 5 & 0 \\3 & 4 & 6\end{bmatrix}\) | |
| 10. |
Which of these statements is incorrect about iterative methods? |
| A. | Low computational cost |
| B. | Low computer storage |
| C. | Not suitable for sparse matrices |
| D. | Needs initial guess |
| Answer» D. Needs initial guess | |