BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

Computational Methods in HighPerformance Computing

Jonathan LandrumMississippi College

December 10, 2014

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

BACKGROUND

High Performance Computing is the use of large computationalsystems to make tight numeric approximations of difficultproblems

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

BACKGROUND

These computational systems range in size from computerclusters with compute core numbers in the range of O(101) toO(102), to supercomputers with compute core numbers fromO(103) upwards of O(106) for some of the recently plannedmachines

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

BACKGROUND

Experience in High Performance Computing comes mainlyfrom two sources:

I Worked with Dr. Magers in the MC ComputationalChemistry Group for three years

I Worked with Dr. Massey at the Coastal and HydraulicsLaboratory over the summer

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

BACKGROUND

Experience in High Performance Computing comes mainlyfrom two sources:

I Worked with Dr. Magers in the MC ComputationalChemistry Group for three years

I Worked with Dr. Massey at the Coastal and HydraulicsLaboratory over the summer

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

BACKGROUND

These two seemingly disparate disciplines have a surprisingamount in common when their computational methods areexamined

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COMPUTATIONAL CHEMISTRY

The Computational Chemistry Group strives to solveSchrodinger’s equation, HΨ = EΨ, in order to find the energyof a chemical system, where:

H = the Hamiltonian operator on the wave functionΨ = the stationary state of the wave function, andE = the energy of the state Ψ

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COMPUTATIONAL CHEMISTRY

The purpose is to find E, which is total energy of the systemrelative to the zero of Coulomb’s law:

~F = ke‖q1‖‖q2‖

r2

where ~F is the force vector, ke is Coulomb’s constant, q1 is the charge of the firstparticle, q2 is the charge of the second particle, and r is their distance.

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COMPUTATIONAL CHEMISTRY

When the distance between the nuclei increases withoutbound, the force between them approaches Coulomb’s zero

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COMPUTATIONAL CHEMISTRY

We only know the Hamiltonian for the system, which has fivecomponents:

H = −Tn − Te − Uen + Uee + Unn

= −∑

i

}2

2me∇2

i −∑k

}2

2mk∇2

k −∑

i

∑k

e2Zkrik

+∑i<j

e2

rij+

∑k<l

e2ZkZlrkl

where i and j run over electrons, k and l run over nuclei, } is Planck’s constant dividedby 2π, me is the mass of the electron, mk is the mass of the nucleus k, ∇2 is theLaplacian operator, e is the charge of the electron, Z is an atomic number, and rab is thedistance between particles a and b.

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COMPUTATIONAL CHEMISTRY

Molecules move and vibrate at extreme speeds

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COMPUTATIONAL CHEMISTRY

Yet the energy of the nuclei, although very high, is essentiallynil when compared to the energy of the electrons

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COMPUTATIONAL CHEMISTRY

Thus, we can simplify Schrodinger’s equation to its electronicversion by reducing the first component to zero and the fifthcomponent to a constant using the Born-Oppenheimerapproximation:

H ≈���>

0

−Tn − Te − Uen + Uee +���>

C

Unn

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COMPUTATIONAL CHEMISTRY

This leaves us to calculate the potential energy of the electrons,the electron-nuclear attraction, and the electron-electronrepulsion

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COMPUTATIONAL CHEMISTRY

Finding the electron-electron repulsion is computationallyintense, thus calculating an exact solution is not practical insystems having more than a single electron

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COMPUTATIONAL CHEMISTRY

We can, however, calculate an approximate solution that iswithin chemical accuracy

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COMPUTATIONAL CHEMISTRY

The method of calculation we employ is the Self-ConsistentField method (SCF) and Density Functional Theory (DFT),which builds a three-dimensional structured grid around thechemical system:

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COMPUTATIONAL CHEMISTRY

With this method, there is a trade-off between the time to thesolution and the accuracy of the results based on the number ofnodes in the grid

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COMPUTATIONAL CHEMISTRY

This calculation allows us to extrapolate E using statisticalmethods

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COMPUTATIONAL CHEMISTRY

Knowing E, we use that value to find:I d

drkE, which gives us optimum equilibrium geometries

I d2

d2rkE, which gives us harmonic vibrational frequencies

I With these we can extrapolate the Gibbs free energies

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COMPUTATIONAL CHEMISTRY

Knowing E, we use that value to find:I d

drkE, which gives us optimum equilibrium geometries

I d2

d2rkE, which gives us harmonic vibrational frequencies

I With these we can extrapolate the Gibbs free energies

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COMPUTATIONAL CHEMISTRY

Knowing E, we use that value to find:I d

drkE, which gives us optimum equilibrium geometries

I d2

d2rkE, which gives us harmonic vibrational frequencies

I With these we can extrapolate the Gibbs free energies

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COASTAL ENGINEERING

My work with the Coastal Processes branch of the Coastal andHydraulics Laboratory this summer was primarily focused ondetermining storm surge inundation

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COASTAL ENGINEERING

We attempted to perfect a model that could accurately calculatethe surge of historic storms:

I Anticyclonic extratropical storms

I Hurricane KatrinaI Hurricane Sandy

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COASTAL ENGINEERING

We attempted to perfect a model that could accurately calculatethe surge of historic storms:

I Anticyclonic extratropical stormsI Hurricane Katrina

I Hurricane Sandy

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COASTAL ENGINEERING

We attempted to perfect a model that could accurately calculatethe surge of historic storms:

I Anticyclonic extratropical stormsI Hurricane KatrinaI Hurricane Sandy

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COASTAL ENGINEERING

While also accurately predicting the surge of coming storms:I Hurricane Arthur

I Hurricane BerthaI Hurricane CristobalI Unnamed tropical depressions

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COASTAL ENGINEERING

While also accurately predicting the surge of coming storms:I Hurricane ArthurI Hurricane Bertha

I Hurricane CristobalI Unnamed tropical depressions

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COASTAL ENGINEERING

While also accurately predicting the surge of coming storms:I Hurricane ArthurI Hurricane BerthaI Hurricane Cristobal

I Unnamed tropical depressions

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COASTAL ENGINEERING

While also accurately predicting the surge of coming storms:I Hurricane ArthurI Hurricane BerthaI Hurricane CristobalI Unnamed tropical depressions

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COASTAL ENGINEERING

We calculated storm surge using an amalgam of in-housesoftware and software from other vendors, and we piecetogether the output of these programs to form our surgeprediction

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COASTAL ENGINEERING

This amalgam currently consists of:I ADCIRC (The ADvanced CIRCulation Model)

I STWAVE (STeady State spectral WAVE)

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COASTAL ENGINEERING

This amalgam currently consists of:I ADCIRC (The ADvanced CIRCulation Model)I STWAVE (STeady State spectral WAVE)

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COASTAL ENGINEERING

Future work will include data from other programs, such as:I ACES (Automated Coastal Engineering System)

I WAM (WAve prediction Model)I Other models as they are developed

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COASTAL ENGINEERING

Future work will include data from other programs, such as:I ACES (Automated Coastal Engineering System)I WAM (WAve prediction Model)

I Other models as they are developed

BACKGROUND COMPUTATIONAL CHEMISTRY COASTAL ENGINEERING CONCLUSION

COASTAL ENGINEERING

Future work will include data from other programs, such as:I ACES (Automated Coastal Engineering System)I WAM (WAve prediction Model)I Other models as they are developed

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COASTAL ENGINEERING

The models we employed used an unstructured grid of thebathymetry of the Atlantic basin:

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COASTAL ENGINEERING

Using an unstructured grid allows for more detail where itmatters, while not burdening the computer with calculatingfine detail in areas that do not matter

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COASTAL ENGINEERING

Calculation of storm surge involves taking into account all ofthe pertinent parameters of the system, including wave height,wind speed, wind direction, bathymetry, and structures such aslevees

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COASTAL ENGINEERING

Because the problem is highly parameterized, the quality of theprediction is directly dependent on the accuracy of these inputdata

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CONCLUSION

“All science is computer science.”

—George Johnson

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REFERENCES

1. “Application Development at LLNL.” Lawrence Livermore National Laboratory.https://computation.llnl.gov/project/SAMRAI/applications.php.

2. Bunya, S., J. C. Dietrich, J. J. Westerink, B. A. Ebersole, J. M. Smith, J. H.Atkinson, and H. J. Roberts, et al. 2010. “A High-Resolution Coupled RiverineFlow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisianaand Mississippi. Part I: Model Development and Validation.” Monthly WeatherReview 138, no. 2: 345-377. Academic Search Premier, EBSCOhost (accessedDecember 8, 2014).

3. Cramer, Christopher J. Essentials of Computational Chemistry: Theories and Models.2nd ed. West Sussex: John Wiley & Sons, 2004.

4. “Example: Hindcast Hurricane Betsy.” ADCIRC Development Group at theUniversity of Notre Dame. Last modified February 21, 2006.http://www3.nd.edu/˜adcirc/betsy.htm.

5. Foresman, James B., and Æleen Frisch. Exploring Chemistry with ElectronicStructure Methods. Pittsburgh: Gaussian, Inc., 1996.

6. Serway, Raymond A. Physics For Scientists & Engineers. Philadelphia: SaundersCollege Publishing, 1990.

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ACKNOWLEDGEMENTS