Exploiting the tensor product structure of hexahedral elements expresses the volume operations as 1D operators. The details are presented in algorithm \ref{alg_hexvol}.

\begin{algorithm}[h]

\caption{Hexahedron volume kernel}

\label{alg_hexvol}

\KwIn{nodal value of solution $\mathbf{u} = \left(p, \mathbf{v} \right)$, volume geometric factors $\partial (rst)/ \partial (xyz)$, 1D derivative operator $D_{ij} = \partial \hat{l}_j /\partial x_i$, model parameters $\rho, c$}

\KwOut{volume contributions stored in array $\mathbf{r}$}

\For{each element $e$}

{

\For{each volume node $x_{ijk}$} { Compute derivatives with respect to $r,s,t$ $$\frac{\partial \mathbf{u}}{\partial r} = \sum_{m=1}^{N+1}D_{im} \mathbf{u}_{mjk} \qquad \frac{\partial \mathbf{u}}{\partial s} = \sum_{m=1}^{N+1}D_{jm} \mathbf{u}_{imk} \qquad \frac{\partial \mathbf{u}}{\partial s} = \sum_{m=1}^{N+1}D_{km} \mathbf{u}_{ijm}$$ Apply chain rule to compute $\partial \mathbf{u}/\partial x, \partial \mathbf{u}/\partial y, \partial \mathbf{u}/\partial z$ $$\frac{\partial \mathbf{u}}{\partial x} = \frac{\partial \mathbf{u}}{\partial r} \frac{\partial r}{\partial x} + \frac{\partial \mathbf{u}}{\partial s} \frac{\partial s}{\partial x} + \frac{\partial \mathbf{u}}{\partial t}*…show more content…*

Revisiting figure \ref{GLNodes}, we notice that the SEM nodal points already contain the surface cubature points while the GL nodes do not. Therefore, the SEM implementation is able to utilize the nodal values to compute the numerical flux, while the GL implementation requires additional interpolations. In algorithm \ref{alg_hexsuf}, we present the procedure of the hexahedron surface kernel. In both implementations, the solution values on the surface cubature points are pre-computed and stored in array \texttt{fQ}. The lines and variables marked with GL/SEM are the processes only needed by the GL/SEM implementation

\begin{algorithm}[h]

\caption{Hexahedron volume kernel}

\label{alg_hexvol}

\KwIn{nodal value of solution $\mathbf{u} = \left(p, \mathbf{v} \right)$, volume geometric factors $\partial (rst)/ \partial (xyz)$, 1D derivative operator $D_{ij} = \partial \hat{l}_j /\partial x_i$, model parameters $\rho, c$}

\KwOut{volume contributions stored in array $\mathbf{r}$}

\For{each element $e$}

{

\For{each volume node $x_{ijk}$} { Compute derivatives with respect to $r,s,t$ $$\frac{\partial \mathbf{u}}{\partial r} = \sum_{m=1}^{N+1}D_{im} \mathbf{u}_{mjk} \qquad \frac{\partial \mathbf{u}}{\partial s} = \sum_{m=1}^{N+1}D_{jm} \mathbf{u}_{imk} \qquad \frac{\partial \mathbf{u}}{\partial s} = \sum_{m=1}^{N+1}D_{km} \mathbf{u}_{ijm}$$ Apply chain rule to compute $\partial \mathbf{u}/\partial x, \partial \mathbf{u}/\partial y, \partial \mathbf{u}/\partial z$ $$\frac{\partial \mathbf{u}}{\partial x} = \frac{\partial \mathbf{u}}{\partial r} \frac{\partial r}{\partial x} + \frac{\partial \mathbf{u}}{\partial s} \frac{\partial s}{\partial x} + \frac{\partial \mathbf{u}}{\partial t}

Revisiting figure \ref{GLNodes}, we notice that the SEM nodal points already contain the surface cubature points while the GL nodes do not. Therefore, the SEM implementation is able to utilize the nodal values to compute the numerical flux, while the GL implementation requires additional interpolations. In algorithm \ref{alg_hexsuf}, we present the procedure of the hexahedron surface kernel. In both implementations, the solution values on the surface cubature points are pre-computed and stored in array \texttt{fQ}. The lines and variables marked with GL/SEM are the processes only needed by the GL/SEM implementation

Related

- Satisfactory Essays
## Nt1330 Unit 6 Report

- 446 Words
- 2 Pages

4.2.2.4 Update Rollup 6 for System Center 2012 R2 Virtual Machine Manager The VMM service crashes and generates an access violation error in System. Xml when it response to an Integration Services event.

- 446 Words
- 2 Pages

Satisfactory Essays - Decent Essays
## Nt1330 Unit 1 Assignment 1 Summary

- 529 Words
- 3 Pages

Summary For the creation of the first database HandsOnOne in a new Query Editor window, first, I went to the SQL Server Management Studio in the program menu and make sure to connect to the named instance SQLSERVERHOA. After the successful connection to the named instance, I went to the Object

- 529 Words
- 3 Pages

Decent Essays - Satisfactory Essays
## Nt1310 Unit 1 Research

- 283 Words
- 2 Pages

In Unit 1 Planning 10, I learned about various web 2.0 tools; e-mail (message), wordle,digital display,video tool, and sound tools. They all help to express yourself but they are used in different occasions. E-mail is used to communicate with a certain people through words. It is very convenient to "talk" to someone far away. The advantage of wordle is that you can introduce yourself with just one logo. Colours, arrangement and style of words involve in the overall impression. Digital display is great when you want to show photos and pictures together with words. Posters and presentaions can easily draw peoples' attention. The unique point of sound byte is that it only contains sound and there are no images to support it. Your skill of talking

- 283 Words
- 2 Pages

Satisfactory Essays - Decent Essays
## Nt1310 Unit 9 Final Report

- 1164 Words
- 5 Pages

When dealing with the calculation and determine the compliance of this scenario you must always follow the surface coating rules and guidelines that has to formulated on a basis of Chapter 106 , which is found in the guidelines of Title 30 Texas Administration Code in

- 1164 Words
- 5 Pages

Decent Essays - Satisfactory Essays
## Nt1310 Unit 1 Assignment 1 Final Report

- 240 Words
- 1 Pages

hi, I have found that you have some remaining spot in organic chemistry 1 problem solving course during Mondays 12 to 12:50 pm . I highly request you to add me or enroll me in this course through registration adjustment process.?

- 240 Words
- 1 Pages

Satisfactory Essays - Satisfactory Essays
## Nt1310 Unit 2 Summary

- 231 Words
- 1 Pages

With the development of the act, laws and regulations addressing issues associated with the prevention, responds and payment of oil pollution were put in place. Such laws and regulations mandated new requirements for companies and their associated personnel involved in the shipment or extraction of oil, such as prevention and response plans, routine documentation and licensing renewal, and evidence of personnel’s competency and knowledge. The act also revised the staffing standards of all foreign shipment vessels, thereby requiring all foreign vessels to meet U.S standards to gain entry into U.S territory. Additionally, these prevention laws and regulations required new standards for shipment vessels and routine inspections. Due to the extreme

- 231 Words
- 1 Pages

Satisfactory Essays - Decent Essays
## Nt1330 Unit 1 Problem Analysis

- 567 Words
- 3 Pages

Users are frustrated by msinfo32.exe. mui related issues like faulty msinfo32.exe free download on Windows 7, 8, msinfo32 exe missing or error in command line, missing from location. These issues are resolved by the msinfo32.exe error repair tool from VSKSoft.

- 567 Words
- 3 Pages

Decent Essays - Satisfactory Essays
## Nt1310 Unit 3 Challenges Paper

- 155 Words
- 1 Pages

In addition Igure et al.[20] specify three challenges that must be addressed to strengthen SCADA networks. The first

- 155 Words
- 1 Pages

Satisfactory Essays - Decent Essays
## Nt1330 Unit 1 Assignment 1 Algorithm Essay

- 461 Words
- 2 Pages

The algorithm is executed by the owner to encrypt the plaintext of $D$ as follows:

- 461 Words
- 2 Pages

Decent Essays - Decent Essays
## Nt1330 Unit 3 Summary

- 318 Words
- 2 Pages

There are also some risks associated with using Indiegogo as a crowdsourcing platform, despite the various advantages provided to HP. As Indiegogo is an online platform, it is indicated that the platform is indeed accessible on a global scale. This means that HP will have to manage a large scale of workers, all around the world. This would require synchronous virtual group meetings and a highly effective two-way information stream where HP is kept informed of all progress and activities being done. This may pose communication barriers decrease the efficiency of meeting goals effectively, which the opposite of what HP is looking to do. Hence, HP’s time would be spent more on management than solution. There is also a problem with the fees associated

- 318 Words
- 2 Pages

Decent Essays - Satisfactory Essays
## Nt1310 Unit 1 Case Study 1

- 583 Words
- 3 Pages

Case 1A Although no one saw the incident morally I would do the right thing and wait for the owner of the car to come back. I would at least wait for a half an hour to see if the person whose car I hit by accident comes back. If for any reason the person has not come back to their vehicle, I would write down my information and place it in their windshield. Morally I feel that it would not be okay for me to ignore the incident that just happened. I was race in a family that taught me the principle of honesty. They taught me that if we ever do a mistake we have to face the consequences of our mistakes even if it was an accident. Although there was no damage to the car, I would still feel obligated to tell the person about the incident. If the scenario was to be turn around I would of want the person to do the same thing for me.

- 583 Words
- 3 Pages

Satisfactory Essays - Decent Essays
## Nt1310 Unit 5 Report

- 666 Words
- 3 Pages

The receiving coil was connected in parallel to the coupling capacitors of 100nF. These capacitors helps the coils to improve coupling co-efficient.

- 666 Words
- 3 Pages

Decent Essays - Satisfactory Essays
## Nt1310 Unit 1 Summary

- 325 Words
- 2 Pages

• The first unmanned satellite called “Sputnik 1” launched and sent to the space by Soviet Union in 1957.

- 325 Words
- 2 Pages

Satisfactory Essays - Decent Essays
## Nt1330 Unit 1 Algorithm

- 662 Words
- 3 Pages

Brief: We were assigned to construct a software that utilizes a classification algorithm that is able to accurately decide a correct classification for a certain sequence of inputs that were provided by the user. The input is to be classified based on a known training set of records of the same attributes as the sequence provided by the user.

- 662 Words
- 3 Pages

Decent Essays - Better Essays
## Design and Analysis of a Laminated Composite Tube

- 2183 Words
- 9 Pages

(5) Thus the bending moments are as follows: (6) {N} and {M} are the generalised stresses can can be expressed as membrane strains and curvatures by using the laminar stress-strain relationship and Love Kirchhoff hypothesis.

- 2183 Words
- 9 Pages

Better Essays