Finite Element Method Questions and Answers – Gaussian Elimination

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This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Gaussian Elimination”.

1. Gaussian elimination is a name given to a well known method of solving simultaneous equation by successively eliminating _________
a) Variables
b) Equations
c) Unknown
d) Algorithms

Explanation: Gaussian elimination is an approach for solving equations type of Ax=B in matrix form. Gaussian elimination is a name given to a well known method of solving simultaneous equation by successively eliminating Unknowns.

2. Step number in Gaussian elimination is denoted as ___________
a) Superscript
b) Subscript
c) Unknown
d) Elimination

Explanation: Gaussian elimination is an algorithm for solving systems of linear equations. The idea at step 1 is to use equation 1 (first row) in eliminating x1 from remaining equations. We know the step numbers as superscript set in parentheses.

3. In Gaussian elimination, A is defined as symmetric matrix then its multiplier is defined as ____
a) C = akk/aik
b) C = aki/akk
c) C = aik/akk
d) C = akk/aki

Explanation: In a Gaussian elimination, If A is a symmetric matrix then its algorithm can be modified in two methods, one method is its multiplier is defined as C = aki/akk. 2nd modification is related to DO LOOP.
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4. A banded matrix is defined as ____________
a) Non zero elements are contained in band
b) Zero elements are contained in a band
c) Non zero elements are contained out of a band
d) Both Non zero elements and Zero elements

Explanation: A band matrix is a sparse matrix whose non zero entries are confined to a diagonal band. In a banded matrix, all of the non zero elements are contained within a band; outside of the band all elements are zero.

5. In a symmetric banded matrix __________
a) aij=aji
b) aji*aij
c) aij≠aji
d) aii=ajj

Explanation: For a symmetric banded matrix aij=aji. A symmetric banded matrix is a symmetric matrix whose nonzero elements are arranged uniformly near the diagonal.

6. Consider a nxn symmetric matrix: $$\begin{array}{c} & \begin{array}{c c c c c c c c c} \underleftrightarrow{\quad \quad n b w\quad \quad} & & & & & & & &\\ \end{array} \\ & \left[ \begin{array}{c c c c c c c c c} x & x & x & x \\ & x & x & x & x \\ & & x & x & x & x \\ & & & x & x & x & x \\ & & & & x & x & x & x \\ & & & & & x & x & x & x \\ \end{array} \right] \end{array}$$ here nbw is called as ______
a) Full band width
b) Half band width
c) Semi band width
d) Co band width

Explanation: In semi banded matrix of nxn matrix nbw is denoted as Half band width of the matrix. By this we can easily be solved further. The term band or banded matrix is used for a matrix whose band width is reasonably small.

7. The line separating from the top zeros from the first non-zero element is called ____
a) Equation
b) Gaussian solution
c) Skyline solution
d) Both Gaussian and skyline solutions

Explanation: If there are zeros at the top of the column, only the elements starting from the first non zero value need be stored. The line separating from the top zeroes from the first non- zero element is called Skyline solution.

8. Frontal method is a _______ of Gaussian elimination method that uses the structure of finite element problem.
a) Structure
b) Variation
c) Algorithm
d) Data

Explanation: Frontal method is a variation of Gaussian elimination method that uses the structure of finite element problem. Elements can be stored in-core in a clique sequence as recently proposed by areas, this subset is called front and it is essentially the transition region between the part of the system already finished.

9. Frontal method is implemented for ________
a) Hexahedral element
b) Polyhedral element
c) Octahedral element
d) Both Hexahedral and Polyhedral

Explanation: The frontal method is implemented for the hexahedral element. By this method we can recombine tetrahedral element to hexahedral element. However, non conformal quadrilateral faces adjacent to triangular faces.

10. Frontal method involves __________
a) Computer programming
b) Manual programming
c) C- programming
d) Computing

Explanation: The elimination process is handled by writing the eliminated equation to the computer hard disk. Processing the front involves dense matrix operations, which use the CPU efficiently. In a typical implementation, only the front is in memory while factors in decomposition are written into files.

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