本田財団レポート No.150
第 34 回本田賞授与式 記念講演（2013 年 11 月 18 日）「第３の科学～計算力学がもたらす科学技術革新～」
テキサス大学オースティン校計算工学・科学研究所（ICES）設立所長、教授

ティンズリー・オーデン博士

THE THIRD PILLAR: The Computational Revolution of
Science and Engineering
Commemorative lecture at the 34th Honda PrizeAward Ceremony on the 18th November 2013

Dr. J. Tinsley Oden
Ph.D., Founding Director of the Institute for Computational Engineering andSciences (ICES), The University of Texas at Austin

ティンズリー・オーデン博士
テキサス大学オースティン校計算工学・科学研究所(ICES)設立
所長、教授
Ph.D., Founding Director of the Institute for
Computational Engineering and Sciences(ICES),The University of Texas at Austin

Dr. J. Tinsley Oden

■生まれ
1936年12月25日 ルイジアナ州アレクサンドリア生(アメリカ国籍)■BORN
December 25, 1936 in Alexandria, Louisiana, USA(USA citizenship)

■学 歴
1959年

■EDUCATION AND TRAINING
1962
Ph.D., Oklahoma State University, Engineering
Mechanics
1960
M.S., Oklahoma State University, Civil Engineering

ルイジアナ州立大学土木工学科卒業

1960年

オクラホマ州立大学土木工学科修士課
程修了

1962年

オクラホマ州立大学機械工学科博士課
程修了

■名誉学位
1987年

ポルトガル・リスボン工科大学より
名誉博士号

1959

B.S., Louisiana State University, Civil Engineering■HONORARY DEGREES
2010
Ohio State University
Honoris Causa

2000年

ベルギー・モン理工科大学より
名誉博士号

2006

Ecole Normale Superieure Cachan (ENSC), France
Honoris Causa

2001年

ポーランド・クラクフ工業大学より
名誉博士号

2004

The University of Texas at Austin
Presidential Citation

2004年

テキサス大学オースティン校にて
学長表彰

2001

Cracow University of Technology, Poland
Honoris Causa

2006年

フランス・カシャン高等師範学校より
名誉博士号

2000

Faculte Polytechnique de Mons, Mons Belgium
Honoris Causa

2010年

オハイオ州立大学より名誉博士号

1987Technical University of Lisbon, Lisbon, Portugal
Honoris Causa

■職 歴
1959年

ルイジアナ州立大学助手

1961年～63年

オクラホマ州立大学応用力学科講師、土木工学科准教授

1963年～64年

General Dynamics 社勤務（研究部門構造担当シニア技師）

1964年9月～73年８月アラバマ大学ハンツビル校
機械工学科 助教授～教授

1973年9月～現在

テキサス大学オースティン校
航空宇宙工学/機械工学科教授

1974年9月～現在

テキサス大学オースティン校
計算工学・科学研究所(ICES)所長(1974-1993 TICOM, 1993-2003 TICAM)

1981年9月～現在

テキサス大学オースティン校
数学科教授

2003年3月～現在

テキサス大学オースティン校研究担当副校長

2011年～現在

テキサス大学オースティン校
コンピューター科学科教授■EMPLOYMENT HISTORY
University of Texas-Austin, Director, Institute for Computational
Engineering and Sciences (ICES), (TICOM 9/1974 - 8/1993, TICAM
9/1993 - 2/2003) 3/2003 - present.
University of Texas-Austin, Associate Vice President for Research,
3/2003 - present.
University of Texas-Austin, Professor, Computer Science
Department, 2011 - present.
University of Texas-Austin, Professor, Mathematics Department,
9/1981 - present.
University of Texas-Austin, Professor, Aerospace Engineering andEngineering Mechanics Department, 9/1973 - present.
University of Alabama-Huntsville, Assistant Professor andProfessor in Engineering Mechanics, 9/1964 - 8/1973.
General Dynamics, Senior Structures Engineer, Research
Department, Fort Worth, 1963-64.
Oklahoma State University, Instructor in Applied Mechanics,
Assistant Professor in Civil Engineering, 1961 - 63.
Louisiana State University, Teaching Assistant, 1959.

■略 歴オーデン博士は工学、数学、そしてコンピューター科学を統合し、自然科学の世界にコンピューター・シミュレーシ
ョンを生み出した、計算力学の創設と発展に多大な貢献をしたことで国際的な名声を得ている。このようなシミュレーションは、医学、材料工学、エネルギー探査そして気候科学など様々な分野で活用されている。現在博士はテキサ
ス大学オースティン校において計算工学・科学研究所所長
として、半導体モデルと癌治療に主眼を置いたマルチスケ
ール“アダプティブ”モデルの研究を進めている。また、
アメリカ土木学会のカルマンメダル(1992年)、アメリカ計算力学学会のニュウマンメダル(1993年)、国際計算力学連合のニュートン・ガウスメダル(1994年)、アメリカ機械学会のティモシェンコメダル(1996年)他多数を受賞している。

■BIOGRAPHICAL SKETCH
J. Tinsley Oden is world renowned for his contributions inestablishing and developing the field of computational mechanics,
which applies mechanics, mathematics, and computer science tocreate computer models of the physical world. Such simulations areused in fields as diverse as medicine, material engineering, energy
exploration, and climate science. As the Director of the Institute for
Computational Engineering and Sciences, Dr. Oden’s current
research is in multi-scale “adaptive” modelling, with a focus on
semiconductor modelling and cancer treatment. For his scientificcontributions, Dr. Oden was awarded the Theodore von Karman
Medal of American Society for Civil Engineers in Engineering
Mechanics in 1992, the John von Neumann Medal of U.S.
Association for Computational Mechanics in 1993, theNewton-Gauss Congress Medal of International Association for
Computational Mechanics in 1994, and The Stephen P. Timoshenko
Medal of American Society of Mechanical Engineers in Applied
Mechanics in 1996, among others.

■出版物“Mechanics of Elastic Structures”:
McGraw-Hill, New York City, 1967年■PUBLICATIONS
Mechanics of Elastic Structures :McGraw-Hill, New York City, 1967

“非線形連続体の有限要素法”:
McGraw-Hill, New York City, 1972年

Finite Elements of Nonlinear Continua :McGraw-Hill, New York City, 1972

“Finite Elements vol.1 to 6”:(E.B Becker および Graham F. Carey 共著)
Prentice-Hall, Englewood Cliffs, 1981年

Finite Elements vol.1 to 6 :(with E.B Becker and Graham F. Carey)
Prentice-Hall, Englewood Cliffs, 1981

“Applied Functional Analysis, 2nd ed.”:(L. F. Demkowicz 共著)
CRC Press, Boca-Raton, 2010年

Applied Functional Analysis, 2nd ed. :(with L. F. Demkowicz)
CRC Press, Boca-Raton, 2010

“An Introduction to Mathematical Modelling”:
Wiley, Hoboken, 2011年

An Introduction to Mathematical Modelling :Wiley, Hoboken, 2011

(27冊の著作を含め、800にも及ぶ論文、記事の中から抜粋)(selected among 800 publications, including 27 books)

このレポートは、2013 年 11 月 18 日 東京、帝国ホテルにおいて行なわれた第 34 回本田賞授与式記念講演の要旨をまとめたものです。
This report is the gist of the commemorative lecture at the 34th Honda Prize Award Ceremony at the Imperial Hotel, Tokyo on
18th November 2013.

THE THIRD PILLAR:
The Computational Revolution of Science and Engineering
J. Tinsley Oden

I am truly humbled by this great honor bestowed on me by the Honda Foundation. This
extraordinary ceremony, the participation of such distinguished guests, and the honor of being
included as part of the great tradition of the Honda Prize represent events marking the peakof one’s professional life. This is truly the high point of my career as a computational scientist,an engineer, a mathematician, and a researcher. I give my sincere thanks to the Honda
Foundation, Mr. Hiroto Ishida, President of the Honda Foundation and to the selection
committee for kindly selecting me and my work for this award. I convey my sincere
appreciation to Mr. Fumihiko Ike, Chairman and Representative of the Honda Motor
Company, Ltd. I also thank other distinguished guests who took the time to attend thisceremony and share with me this special event. I am particularly grateful to Mr. Satoshi
Matsuzawa, Managing Director of the Honda Foundation, whose kindness and professional
assistance made this occasion all the more enjoyable. And I thank my dear friends here whohave interacted with me professionally and socially over the years who are part of my mostrespected supporters. Thank you all for attending this ceremony.
I also embrace the ecotechnology concept of the Honda Foundation, and hope to lay downarguments that computational mechanics—and more broadly, computational science—hashad, and will continue to have, a profound impact on all of science and technology, and will
emerge as an indispensable factor in preserving our precious ecological systems andadvancing ecotechnologies in the future.

34

I am indebted to many individuals who supported me and my work on the long path thatbrought me to this point in my life: my family, my wife Barbara, son Walker, and daughter
Lee, who patiently and lovingly sacrificed time with me so I could do my work; to my parents,
who encouraged me as a child and an adult to devote myself to scholarship and research; andto many students, postdocs, and professional colleagues, some of whom are here at thisceremony, who collaborated and supported much of my work over the years.

■ Table of Contents

Fig 1〈Fig 1〉This presentation is divided into the nine topics indicated here, beginning with

the introductory comments I make now.

35

■ Foundations of Science and Engineering

Fig 2〈Fig 2〉

I begin this lecture with a few comments on ancient subjects of concern to all of us

here: science, the scientific method, and its application to problems affecting mankind. A
simple definition of science is this: the activity concerned with the systematic acquisition ofknowledge. The English word is derived from scientia, which is Latin for “knowledge.”
According to the Cambridge Dictionary, it is “the enterprise that builds and organizes
knowledge in the form of testable explanations and predictions about the universe.” It is
designed to reduce or eliminate ignorance by acquiring and understanding information andinvolves the mental comprehension of perceived truth or fact through cognition. Engineeringis the systematic application of scientific and practical knowledge for the benefit or needs ofmankind.
Few doubt the importance of scientific discoveries and the enormous advances they havemade possible in technology over the last millennium in improving the welfare, safety,
longevity, and richness of life of the human species. With advances in science, comesunderstanding of the universe in which we live, the forces and laws that govern it, andultimately the ability to control those forces and direct them in a way to benefit humankind.
I believe that to dedicate one’s time and energy to science, that is, to acquire knowledge,
and more importantly to apply it, is one of the most honorable activities in which one canengage, but, it is also an activity that is enormously challenging, and, at the same time,
remarkably exhilarating.

36

■ An Ancient Question and Debate

Fig 3〈Fig 3〉The question of how knowledge is acquired has been a subject of debate among

philosophers of science for almost 3,000 years. We find, from the writings of Plato on Socrates,
the great philosopher who lived between 469-399 BC, that Socrates believed that knowledge
lies in the immortal soul. Not trusting the human senses, he believed that knowledge occurs
by recollection or divine insight, and Plato, his student, aggressively perpetuated thatthinking. But Plato’s student, Aristotle, who lived between 384–322 BC, had a more appealing
answer: knowledge is acquired by reasoning and demonstration—a precursor to the idea thatphysical observation and inductive hypothesis create knowledge. In the two millennia between
500 BC and the 15th century, we had the likes of Archimedes, da Vinci, and others. Sir
Francis Bacon, David Hume, Galileo, Newton, and others followed in the 16th-18th centuries,
and then, in the 20th century, there was Dirac, Eddington, Bohr, Einstein, Maxwell,Boltzmann, and many more.
Sir Francis Bacon, who is credited with influencing the dawn of the industrial age, put forth
the idea that everything is learned by induction and organized observations. This notion wasaddressed by the British philosopher David Hume, who founded the philosophy of skepticism,based on the proposition that induction cannot lead to knowledge. Knowledge, according to
Hume, can only be obtained through observation and experiment. By induction, we mean thedevelopment of hypotheses, generally theories, based on interpretations of causes ofobservations of physical events, and, then extrapolating from those hypotheses to forecast
future events, or events in the past.

37

Ultimately, the great scientists of the 19th and 20th centuries, ignoring or oblivious to the
pessimism of Hume, continued to develop inductive theories that changed the world. But thephilosophical foundations were still unsettled until the work of Karl Popper, the 20th century
philosopher, who put forth his principle of falsification, to wit: an inductive hypothesis, atheory, cannot qualify as a true scientific theory unless it were possible to falsify it throughobservations contrary to predictions; that is, unless it were possible to acquire observations
that could be in conflict with the theory. Without the possibility of falsification, the hypotheses
were pseudo-science and not a true scientific theory. Once falsified, the theory could be
modified to agree with observations or discarded. And so we came to recognize that a scientifictheory, a product of induction, is only valid as long as it is not contradicted by physicalobservations. A mathematical theory, on the other hand, which arises from deductive
reasoning (the establishment of axioms and then using mathematical logic to prove theconsequences of those axioms) is permanent and unfailing, and does not change. Thus, correctmathematical proofs last forever; scientific proofs last only until they are contradicted byobservations. Even Popper was eventually criticized as being too objective. It was said that thephilosophy of objectivism was not how real science was done. Real observations of the physicaluniverse account for the statistical nature of events, and Popper’s principles, at least earlyversions of them, did not use statistical interpretations.
As the 20th century progressed, we came across the likes of extraordinary scientists who
made inductive contributions to what we know about the physical universe: Rene de Broglie
formalized the relationship between electromagnetic waves and momenta a decade before
these relationships were confirmed experimentally. Also, Paul Dirac, purely on the basis ofmathematical calculations, discovered the existence of anti-matter, a physical reality that was
only observed experimentally a dozen years after his announcement. This led Sir Arthur
Eddington, who confirmed Einstein’s theory of relativity through astronomical observations
long after they had been predicted by the theory of relativity, to comment, “theexperimentalist will be surprised to learn that we will not accept experimental data unless it
is confirmed by theory”. This was clearly opposite to the views of Hume and others. Morerecently, the physicist and probabilist, Edwin T. Jaynes, put forth the notion that all science is
inductive, that an inductive process must be used, even when one wishes to design
experiments, or to assimilate and mine data, or to explain the causes of events observed inexisting physical systems.

38

■ The Classical Pillars of Science

Fig 4〈Fig 4〉Thus, after millennia of debate by the greatest minds of human history, twoavenues to scientific knowledge emerged: 1) observations, experimental measurements,
information gained by the human senses, guided by instruments, and 2) theory, inductive
hypotheses often framed in mathematical language. Observation and theory are thus, the twoclassical pillars of science. According to the Oxford Dictionary, the scientific method is “amethod of procedure that has characterized natural science since the 17th century, consistingin systematic observation, measurement, experience and experiment and the formulation,
testing, and modification of hypotheses.”39

■ Is There a Third Pillar?

Fig 5〈Fig 5〉Is there a third pillar? Is there a new avenue to gain scientific knowledge? The

answer, in my mind, and in the minds of most contemporary scientists and engineers, is veryclearly “Yes.” It is the new discipline of computational science: the use of computers andmodels, computational algorithms, and computing devices to fashion models of how thephysical universe behaves to predict the future, and also reconstruct the past. In little morethan a half century of the two to four million years of human history or, on a historic scale, inthe blink of an eye, the entire scientific landscape has changed forever. Computational scienceis the most important scientific event in human history. It has transformed forever the way
scientific discoveries are made and how engineering applications are performed. It lies at theintersection of mathematics, computer science, and the core disciplines of science andengineering. Mathematics, because it is the language in which scientific theory is written, as
well as the language to transcribe and transfer information on observations, is anindispensable component of the classical pillars of science. Mathematics is also the language
in which the mathematical theories of science are reconstituted and put in a form that can beprocessed by digital computers. Computer science is the body of scientific knowledge andtechnology designed to understand and build computing devices, and to develop the language
and means to communicate with computing machines. Of course, the traditional core
disciplines of science and engineering must now be reviewed and reconstituted because what
had once been out of reach by traditional science is now well within reach because of theadvent of powerful new tools and approaches afforded by computational science.

40Computational science, I submit, is the Third Pillar of Science. It embodies the developmentof computer models, computer simulations, data retrieval and mining, processing of large data
sets, and explicit advances in computing technology. It enables scientific discovery andadvances never thought possible before—in manufacturing, medicine, surgery, materials,
climate science, geophysics, in understanding natural hazards, and many other areas oftechnology and scientific study.

■ Mechanics and Computational Mechanics

Fig 6〈Fig 6〉

My introduction to this subject began by studying mechanics and computational

mechanics, the scientific discipline concerned with the study of the motion of bodies under theaction of forces; so it embraces solid mechanics, fluid mechanics, but now also includes
materials science, the motion of electrons, quantum mechanics, and statistical mechanics. In
my mind, with a clear, broad definition of mechanics, it is indistinguishable fromcomputational science.

41

■ What can CSE do that classical science cannot?

Fig 7〈Fig 7〉

What can computational science and engineering do that classical science cannot?

It can look into the past with inverse analysis, to determine what past events caused observed
phenomena. It can explore the effects of thousands of scenarios for or in lieu of actual
experiments. It can be used to study events beyond the reach of expanding the boundaries ofcontemporary experimental science, such as in drug design, space exploration, climate change,
and natural disasters. It can even explore the consequences of a breakdown in models andtheories. It can optimize procedures for the design of projects and systems.

42

■ The Anatomy of a Computer Simulations

Fig 8〈Fig 8〉Let us now dissect the anatomy of a computer simulation. Exactly what is

involved in applying the tools of computational science to acquire knowledge or to understandthe behavior of engineered systems? First, there is the mathematical model, which is acollection of mathematical constructions that translates both inductive hypotheses about thefunctions and behavior of the physical system, as well as observations of the response of thesystem to various inputs within a mathematical context. Second, there is the computationalmodel, a corrupted discretization of the mathematical model rendering into a form that can beprocessed by computing devices. Third, there are mathematical and computational algorithms
that are step-by-step procedures and formulations used for calculation, data processing, andautomated reasoning. Fourth, there is scientific software that delivers machine-readable
instructions that direct computers to perform specific functions. Then, there is the computer,the device that performs logical operations with quantities represented by digits usually inbinary number systems. Finally, there is the output data, which must be processed andinterpreted and used in predictions or designs or in decision making.

43■ The Anatomy of a Computer Simulation 2

Fig 9〈Fig 9〉A good example of a computer model of a physical phenomenon is that of flow ofwater through a channel. One could assume that the system is governed by the fundamental
laws of conservation of mass, and the principles of conservation and balance of linear andangular momentum. Assuming the laws governing the motion of viscous fluids, one chooses
the renowned Navier Stokes equations as a mathematical model of the physical phenomenon.
For this case, let us select a quantity u for the velocity of the fluid, ߩ as its density, ߥ its
viscosity, a physical parameter, p the pressure, and b the body force, such as might be
represented by the weight of the fluid or its buoyancy. This is a mathematical characterizationof a theory, embodied in the principle of balance of momentum. To render it into a form thatcan be computed, we discretize it: we replace derivatives of functions with discrete
approximations to produce a computational model, and then we develop a code, a computer
program, and implement the solving of the computational model on a computer. This produces
a discrete characterization of the solution of the model that depicts the fluid flow we originally
set out to simulate. There is another step between the production of the computed results andtheir use, and that is to develop, interpret, and visualize the solution, and to use one’s
knowledge to infer the behavior of the system. So, once again, the methods and techniques ofmodern computer science enter the picture.

44

■ The Greatest Modeling Methods and Algorithms of Modern History Made Possible byComputers

Fig 10〈Fig 10〉 What are the methods and algorithms of modern history that have made theseadvances possible? Some modern computational methods would not have existed without theadvent of computers. The first I will mention is the finite element method. Generally regarded
as having been created in the 1950s, with some vestiges of it going back much further, thefinite element method continues to be developed and used extensively today. It is an ingenious
method in which a complex physical problem is divided into small pieces, its finite elements,
and the laws of mechanics are applied to each individual piece. These are then packed
together to form complete models of large, complex systems. The finite element method has
impacted virtually every area of science and technology. I had the good fortune to play a role
during its early years and to develop some of the earliest computer programs that
implemented the method for the analysis of complex aerospace and aeronautical systems.
That was in the early 1960’s. Later, in the 1970’s, I authored one of the earliest books on its
mathematical foundations, a subject which has become a rich and active branch of applied andcomputational mathematics, and is taught worldwide.

45

■ The Greatest Modeling Methods and Algorithms of Modern History Made Possible byComputers 2

Fig 11〈Fig 11〉 Basically, the finite element method enabled the engineering and scientificcommunity to solve partial differential equations on geometrically complex domains, and it ismathematically rigorous. Not only did the ability to solve partial differential equations createa huge impact on modern mathematics, but it also revolutionized engineering. Other methodsof statistics and statistical sampling are enabled by advances in computers and are
manifested in the powerful new algorithms such as the Markov Chain Monte Carlo method,
the use of molecular dynamics to the study of chemistry, the study of statistical methods,
stochastic systems, and so on. These fields would never have existed had it not been for theadvances of digital computing and computational mathematics in the 1980s and 1990s. Now
these statistical sampling methods are becoming fundamental tools in many areas of scienceand engineering. Molecular dynamics simulations are used in biology, in the understanding of
the behavior of viruses and bacteria, in the development of nanoparticles for drug delivery,
and in engineering new materials. These are computational algorithms that model nature at
an atomistic or molecular level. They have had a tremendous impact on how we understand,teach, and use modern biology, chemistry, and physics. Next is the Density Functional Theory,a theory of quantum systems that led to the development of a revolutionary reformulation ofquantum mechanics that brought a host of new methods to solve problems at the electroniclevel and to the study of first principles in the behavior of materials and physical systems.
More recently, several new, very fast algorithms have been designed that enable the solutionof very large problems with billions of unknowns in a fraction of the time of the methodologies
and algorithms that were available back in the 1980s and 1990s. These have led to hugeadvances in such fields as seismology that help find and exploit vital reserves in oil and gas.

46

■ Are Advances in Computational Science Strictly Due to Advances in the Size andSpeed of Computers?

Fig 12〈Fig 12〉 In viewing these scientific advances brought about by computing, one may ask:
can all of these be attributed strictly to advances in the size and speed of computers? I mustregister emphatically a resounding “No” to this question. Many, many counterexamples can beregistered. The graph shown indicates that if one plots the effective gigaflops on a computing
device against the calendar year in which advances in computer speeds were made, forexample, in proportion to the number of semiconductors per computer chip, this corresponding
increase is roughly linear over the last 30 years, a well-known and documented fact. When one
factors in great advances in algorithms, many of which have already been mentioned, theeffective size, processing speed and complexity of problems, have increased by four orders ofmagnitude. Computers alone have contributed to only a portion of the advances incomputational science in recent years.

47

■ Imperfect Paths to Knowledge

Fig 13〈Fig 13〉 In modern computational science, every phase of the scientific method involves
uncertainty. It is in observations, in data characterizing the models, and in the models
themselves, since they are only mathematical abstractions of reality. There is also uncertainty
due to the discretization of the model which casts it into a form that can be processed by acomputer. The management of all these uncertainties and their quantification and control,using modern methods of statistics and probability, are now at the cutting edge of research incomputational science. While the presence of uncertainty in scientific predictions has beenrecognized for many years, it has only been in recent times that modern algorithms, methods,
and computing machines reached the level of development at which significant advances canbe made to manage these uncertainties, and to control and quantify them. This is a subject I
have been working on steadily over the past decade, and I believe we are close to developing afull and rigorous theory for uncertainty quantification and for creating the foundations ofwhat is called “predictive science.”

48

■ Error Estimation and Adaptivity

Fig 14〈Fig 14〉 And, we now turn to an area related to my earlier comments on the fallibility ofcomputers, models, and even scientific theories in predicting the future. In solving complex
problems, have we developed over the past decades any way to estimate these errors, toreduce them, and to control them? The answer is “Yes,” and, in fact, the whole subject of error
estimations and adaptivity is a huge and important area in computational science and one inwhich I have had the privilege to be involved. The general question is this: if we acknowledge
that theories, models, and computer discretizations and observations are in error, how can one
calculate approximations of error and correct them? The general answer that I have used in
my work is to compute what is called a residual. A residual is leftover information that results
when erroneous answers do not satisfy the equations governing the computational model.
Then one needs to adjust the parameters of the model so that one can prove mathematicallythat the residual is reduced. This is called adaptivity, and adapting the discretizations, or
adapting the model to reduce error, is a fundamental concept that has permeated much of themodern work in computational science, including my own.

49

■ The Last Word: The Path to Truth

Fig 15〈Fig 15〉 The philosopher Hans Reichenbach states in his book The Rise of Scientific
Philosophy that, “If error is corrected whenever it is recognized as such, the path to error isthe path to truth.” This is the underlying philosophy of adaptive computational methods.

■ Examples of CS&E Research at ICES

Fig 16〈Fig 16〉 I would now like to list a few examples of modern applications of computational
science that have been performed at my institute over the last half decade.

50

■ Global Mantle Convection ModelingFig 17〈Fig 17〉 This example is a remarkable calculation of the cooling of the earth’s core and thecreation of the earth’s mantle, a spherical shell exterior to the core modeled as a viscous
creeping incompressible, non-Newtonian fluid. The model involves the fundamental equationsof balance of momentum, mass, and energy. It is this model that was featured in Science

Magazine and, indeed, was on the cover of Science in 2010. It pictures a model of around 300
million hexahedral finite elements, around 1.2 billion degrees of freedom, and solved onaround 5,000-10,000 processor cores of the Ranger super-computer system. The calculation
was done about three years ago by a team at ICES Center for Computational Geosciences andOptimization, led by Omar Ghattas, and took on the order of 100,000 time steps.

51

■ Mantle Convection Simulation

Fig 18〈Fig 18〉 The movie shows that the Earth’s mantle arises from plumes of warm rockflowing buoyantly from the mantle core. The plumes, called upwellings, flow along the earth’s
crust upward. They subsequently cool and break down back into the core of the earth. These
are called downwellings. The round trip of these convection cells is on the order of a few
hundred million years, with a typical flow velocity of a few centimeters per year. Thisphenomena is thought to drive plate motion to the earth’s surface in a very high Reynold’s
number flow, which is very unstable and requires 10 kilometers of resolution of the sharp
thermal fronts and even finer one kilometer resolution at the plate boundaries. This
resolution would lead to an intractable computation since the earth has an excess of around
one trillion cubic kilometers. Adaptive mesh refinement reduces the number of elements
needed by a factor of 5,000. The movie also shows that large thermal gradient regions andregions of large viscosity promote dynamically adaptive meshing to control the resolution ofimportant physical details predicted in the model.
Ultimately, predicting the behavior of the complete dynamical system responsible for platemotion and earthquakes, the creation of volcanoes, mountain ranges, and long-term sea levels
will fill enormous gaps in our knowledge of questions that are basic to principles of driving
and resisting forces of plate tectonics and what is the energy balance of the planet as a whole.
The understanding of mantle convection has been designated as one of the Ten Grand
Research Questions in Earth science. We are building these models to help answer thesequestions.

52

■ Hurricane Storm Surge and Oil Spill Modeling in the Gulf of Mexico

Fig 19■ Hurricane Storm Surge and Oil Spill Modeling Using the ADCIRC CodeFig 2053

■ Hurricane Storm Surge and Oil Spill Modeling – Hurricane Katrina and the
Deepwater Horizon

Fig 21〈Fig 19-21〉 Next, we show the hydrology induced by hurricanes and the prediction of socalled storm surges. This calculation was also done in 2010 by the ICES Computational
Hydraulics Group led by Clint Dawson. The figure shows wind vectors and storm surge
contours during Hurricane Katrina in 2005 that caused extensive flooding in southernLouisiana (Fig 19). The topography and bathymetry is generated using satellite images of thecoast and sea-floor topography. On the right in Fig 21, we show the hypothetical transport ofan oil spill if it had occurred during the storm. The coastal flooding is simulated by a finite
element code called ADCIRC on a mesh of around ten million finite elements. The oil spilltransport is represented by ten million Lagrangian particles. Coastal flooding is simulatedwith a one-second time-step over a span of seven days. It is solved using a fourth-order RungeKutta scheme and interpolating the computer currents over the same span. Had an oil spill
been active during the landfall of Hurricane Katrina, oil would have been pushed further
offshore and very near metropolitan New Orleans. With such calculations, we hope to quantify
the hazards associated with coastal flooding during extreme, natural, and manmade events.

54

■ Nano-Manufacturing – Engineering at the Atomic Scale

Fig 22■ Nano-Manufacturing – Etch Barriers in Step and Flash Imprint Lithography

Fig 2355

〈Fig 22-23〉 Computer modeling and simulation allows one to predict events and design
engineering systems at scales perceptible only by electron microscopy. These types of models
have been developed by my Multi-Scale Modeling Group at ICES and are used to simulate
manufacturing objects at nanometer scales, ranging from nanoparticles for drug delivery to
manufacturing today’s semiconductor devices. It is known that the optimal speed ofcontemporary super computers depends upon the number of semiconductors that can beplaced on a computer chip. So the grand challenge of modern chip design is to develop
processes to produce smaller and smaller semiconductors – but this can only be done withcareful designs and process monitoring of the manufacturing process.
Shown in the figure 22 is an example of a nanomanufactuing process at the nanoscale(which concerns subjects sized at one billionth of a meter, or 1000th the width of a humanhair). The process, called Step and Flash Imprint Lithography, works by depositing aphotocurable acrylate solution on a wafer that is exposed to ultra-violet light through a quartz
template designed to imprint geometric features of tiny semiconductor components. The
template and device involved in the process run upwards of $20 million and must be designedwith precision to produce components of nanodimensions with almost perfect geometricfidelity.
The process of producing the critical etch barriers, shown, is modeled using a huge
computational model of the polymer material (Fig 23). The model is used to define the shapeof key semiconductor components.

56

■ Nano-Manufacturing – One Realization of the Polymerization Process

Fig 24■ Nano-Manufacturing – Multi-Processor Computations

Fig 2557

■ Nano-Manufacturing – Shrinkage Adaptive Step

Fig 26〈Fig 24-26〉

Computer generated molecular structures of the etch barrier are shown,attained using a Monte Carlo algorithm that employs kinetic chemical reaction rates todetermine the most probable molecular situations (Fig 24). These structures are thenintroduced into a molecular dynamics model to compute the deformed shapes of the polymer
barriers, as in the three-million-degree-of-freedom model shown (Fig 25).
A remarkable aspect of this calculation is that multi-scale modeling was used to control
modeling error, resulting in hybrid models of the type shown where part of the structure wasmodeled at a molecular level and part at a macro-scale-continuous level (Fig 26). The resulting
predictions helped optimize the design of the process and minimize flaws in the semiconductor
components. This is an example of adaptive modeling that we developed to control error in
predictions of component behavior.

58

■ Cardiovascular Modeling – Reconstruction of a 3D Anatomically Accurate Heart MitralValve

Fig 27〈Fig 27〉 Next is a very interesting simulation of cardiovascular phenomena developed at
the ICES Cardiovascular Simulation Center under the direction of Michael Sacks. This
computational model is a reconstruction of an anatomically-accurate heart mitral valve. It
was developed from a Micro CT image of around 39.46 microns resolution, with the perfect
voxel resolution in around 1,014 slices. It shows the interior leaflet in red, the posterior leaflet
in green, the chordae tendineaes and papillary muscles in yellow of the heart valve, with halfa million nodes and around two million tetrahedral elements. The simplified model depicts the
motion of the mitral valve this time using around 6,500 shell elements plus hexahedral
elements for the mitral valve chordae tendineaes. The calculation was solved on 24 cores.

59

■ Cardiovascular Modeling – Mitral Valve Simulation

Fig 28〈Fig 28〉 Here we see modeling and closure of the mitral valve due to trans-valvuler
pressure–loading and ending with the thorough validation of the computational model using
in vitro experimental data.

■ Prostate Cancer Research – A DDDAS Model – Cyberinfrastructure and Work FlowFig 2960

■ Prostate Cancer Research – A DDDAS Model – Imaging to Mesh Generation Pipeline

Fig 30■ Prostate Cancer Research – A DDDAS Model – Patient Specific Calibration

Fig 3161

■ Prostate Cancer Research – A DDDAS Model –Treatment Process

Fig 32〈Fig 29-32〉

Here we see a dynamic data-driven application system designed to treat

prostate cancer (Fig 29). The canine patient was placed in an MRI-device and an MRI image
was taken of the infected prostate to be sent, over a high-bandwidth network, to thecomputational arena at ICES where a bioheat transfer model of the 3-D infected gland ismade using finite elements and a model of bioheat transfer (Fig 30). The finite element meshof the prostate shows a catheter inserted to terminate in the vicinity of the cancer cells. A
laser was used to increase temperature in this area. Computational models of cell damage,heat shock protein, and thermal ablation were employed (Fig 31). By modeling the entire
physical event, it is possible to minimize damage to healthy cells and maximize cancer cells inthe vicinity of the catheter. The computational model enabled an adaptive control of the powerof the laser, the resulting temperatures, the thermal environment supplied to the catheter,
and the placement of the catheter in real time during this process. Next, very good agreement
was obtained between the computational model and the experimental data, validating themodels used. This study was conducted by my Multi-Scale Modeling Group at ICES.

62

■ Drug Design – SIV/HIV Envelope Interacting with a Candidate Inhibitor

Fig 33〈Fig 33〉 In the next example, we show results obtained by Chandrajit Bajaj’s group in theComputational Visualization Center at ICES on electrostatic potential computations for atarget-spiked protein GP120 on the envelope of SIV HIV simian immunodeficiency viruses
interacting with a candidate inhibitory protein NIH45-46. HIV uses GP120 as an importantsignaling mechanism to gain simian-human immune T-cell entry. In the movie, theelectrostatic potentials are computed with the Poisson-Boltzman equations initially using
electron tomography for fine atomistic structure modeling of the GP120. Blue denotes positive
potentials, red denotes negative potentials, and the cancelation of positive and negative
potentials helps visualize the electrostatics complimentarity of the target and inhibitor andget the binding affinity.

63

■ HIV RT Synthesizes DNA

Fig 34〈Fig 34〉 As a final example, we use computational methods to explore the secrets of life.
Here, we display a minimum free-energy pathway for the conformational transition of the HIVreverse transcriptase obtained at ICES’s Center for Computational Life Sciences and Biology
directed by Ron Elber. HIV RT is a DNA polymerase with the task of synthesizing a new DNA
molecule according to a template. The conformal transition of the protein when closing of a
nucleotide is displayed. The transition selects the correct nucleotide to be added to the DNA.
It is not completed successfully for the wrong substrate. Here, we were able to pinpoint the
selection and reproduction quantitatively for the rate at which the protein changes its
conformation to within milliseconds. The size of the model is 135,000 atoms. To compute thefree-energy profile required around 10 billion molecular-dynamic steps with 10 femto-seconds
for each time step. It was solved on the Lonestar computer at the Texas Advanced Computing
Center running on 100 cores for over a month. What we see in the movie, is a close up of theprotein active site and the way the protein changes its conformation while closing on thesubstrate. The group in purple is the nucleotide substrate to be added to the DNA in green.
The orange spheres are magnesium ions necessary for the reaction, the yellow moving groups
are positively-charged life sign side chains closing on a negatively charged nucleotide andgetting it ready for chemical processing. What we hope to learn is how the protein selects thecorrect nucleotide to obtain an accurate copy of the original DNA. A conformational transition
locks only on the correct substrate and the simulation makes it possible to quantify thelocking mechanism that determines the rate of reaction in binding energy and thecontribution to the overall precision of the enzyme. Some believe that this model can teach us

64the secrets of life with regard to the behavior of DNA and transport mechanisms. Membranes
separate inside and outside cells, but nevertheless transportation across membranes isnecessary to supply nutrients and eliminate waste products. One transport mechanism ispassive, directly through the membrane, without the assistance of trans membrane proteins.
Passive transport is also relevant for drug delivery. Here we consider the transport of a singleamino acid tryptophan across a DOPC membrane as a model for permeants of moderate size.

■ Acknowledgements

Fig 35〈Fig 35〉 The examples I presented were kindly provided by my collaborators andcolleagues and my group at ICES.

65

■ Summary and Conclusions

Fig 36〈Fig 36〉 We are gradually coming to the realization that this Third Pillar will inevitablychange the way we educate the scientists and engineers of the future, how we organize andperform research, and how we view knowledge and acquire it. The traditional compartmentsof knowledge reflected in our universities and in many industries is now seen to be artificial,
not designed for interdisciplinary activities that are now made relevant and possible by therise of computational science. The old systems will change or be lost in perpetuity.
What you and your children and your grandchildren will learn is that computational science
will enable the study and understanding of things that have eluded scientists and engineersfrom the beginning. Can you study, with precision, events that happened centuries in past?
Can you understand the initial and mechanical conditions that lead to earthquakes andtsunamis? Can you understand the stochastic nature of physical systems and have long-range
predictions of our climate and our weather? Can you understand the nature of subatomic
particles, of electrons, and how they form new materials? What about biological systems, suchas the design and manipulation of new drugs, understanding diseases, the delivery of drugs at
scales that cannot be perceived with the human senses? Can you model and understand thefunctions of the human body, the cardiovascular system, cures for cancer, or how to collect,
store, process, and use the enormous amounts of data required to map out the functions ofindividual human bodies? Computational science has enabled all of these things to be liftedfrom the level of dreams and fiction and they are destined to become true accomplishments ofscience and technology in the future.

■ This report can be viewed in the Honda Foundation’s website.
You may not use the proceedings for the purposes other than personal use without
the express written consent of The Honda Foundation.

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