Concurrency and Computation: Practice and Experience, 2014
We present a graphics processing unit (GPU) parallelization of the computation of the price of ex... more We present a graphics processing unit (GPU) parallelization of the computation of the price of exotic crosscurrency interest rate derivatives via a partial differential equation (PDE) approach. In particular, we focus on the GPU-based parallel pricing of long-dated foreign exchange (FX) interest rate hybrids, namely power reverse dual currency (PRDC) swaps with Bermudan cancelable features. We consider a three-factor pricing model with FX volatility skew, which results in a time-dependent parabolic PDE in three spatial dimensions. Finite difference methods on uniform grids are used for the spatial discretization of the PDE, and the alternating direction implicit (ADI) technique is employed for the time discretization. We then exploit the parallel architectural features of GPUs together with the Compute Unified Device Architecture framework to design and implement an efficient parallel algorithm for pricing PRDC swaps. Over each period of the tenor structure, we divide the pricing of a Bermudan cancelable PRDC swap into two independent pricing subproblems, each of which can efficiently be solved on a GPU via a parallelization of the ADI timestepping technique. Numerical results indicate that GPUs can provide significant increase in performance over CPUs when pricing PRDC swaps. An analysis of the impact of the FX skew on such derivatives is provided. PRDC swaps. The use of a local volatility model provides better modeling for the skewness of the FX rate and at the same time avoids introducing more stochastic factors into the model.
This paper presents the development of a workspace controller for a newly designed platform. The ... more This paper presents the development of a workspace controller for a newly designed platform. The platform is designed to manipulate endoscopic tools and is actuated by tendons to meet the small scale requirements in en-doscopy. The tendon actuation provides challenges to the controller design since the number of degrees of freedom equals the number of tendons. In typical tendon-driven systems, the number of tendons is greater than the number of degrees of freedom. This paper presents the kinematic and dynamic analysis of the manipulator and presents a workspace controller for the tendon driven system. Simulation as well as experimental results are presented for the controlled system. The results demonstrate the eec-tiveness of the controller in tracking a step response and a circular trajectory at 2.0Hz and greater. The device is similar to the Stewart platform and the basic design can be used in applications where the full range of motion of the Stewart platform is not required. Applications of the device range between targeting systems, snake-like robots, and endoscopy.
— During an automobile crash, some parts in the front of an automobile body will have plastic def... more — During an automobile crash, some parts in the front of an automobile body will have plastic deformation and absorb a lot of energy. Hence it becomes necessary to check the car structure for its crash ability so that safety is achieved together with fuel economy. A simple finite element (FE) model of a car is developed in ANSYS and it is solved for full frontal impact in ANSYS LS-DYNA explicit code. Computational simulations and various results are plotted and analyzed. There are various test configurations. We have limited our analysis to frontal impact with a rigid wall at a speed of 35 mph, corresponding to a NHTSA (National Highway Traffic Safety Administration) full frontal impact. It was noted that composite materials could be used more effectively for light-weightiness other than metallic materials without affecting the necessary impact energy absorbing capacity of the car body. Since composite materials and metallic materials absorb approximately the same energy during a car crash we conclude that composite materials can be used for light-weightiness in automobiles.
This book is dedicated to the use of the finite elements method for the approximation of equation... more This book is dedicated to the use of the finite elements method for the approximation of equations having partial derivatives. It resumes part of the curriculum leading to the certificate in “Numerical Methods forMechanics” taught by the author since the past twelve years as part of the graduate studies in Mechanics at the University of Pierre and Marie Curie (Paris VI). Numerical Analysis has undergone a spectacular development during these past forty years. It is most probably related to the boom in InformationTechnologywhich has literally invaded the planet and provided, de facto, calculation capacities undreamt of up to now. This mathematical knowledge field – Numerical Analysis – may be characterised as the “mathematic of mathematics” in the same line of thought as that of a “police of polices”. Indeed, as soon as a mathematical technology cannot be applied within the industrial applications due to operational inadequacy, numerical analysis takes over and finds the solution by identifying the best adapted approximation process. From there on, all other mathematical branches may be used to “force a passage” and to estimate a solution by often combining shrewdness and lucidity within a stringent mathematical framework. Numerical analysis is best and most often applied to the approximation of equations having partial derivatives as a major support to the modelling of real systems. Whether it be applications in physics or in mechanics, in economy, marketing or in the field of finance, the phenomenological translation of the system under study often leads to the resolution of equations having partial derivatives. This justifies the invention of numerous methods to solve such equations. The finite elements method, the finite volumes method, the singularity or integral method, the spectral methods and the variational finite differences method are some of the most popular methods. However, the finite elements are those that definitely and drastically changed the world of numerical approximation of equations having partial derivatives. Having an exceptional flexibility, the finite elements undoubtedly constitute the approximation method that is mostly used in solving mathematical models in engineering sciences. Considering the mathematical technicality required to apply finite elements, many authors specialised in numerical analysis, including Pierre Arnaud Raviart (8), presented the subject at higher level university teaching reserved to students who possess the mathematical prerequisites, particularly in function analysis, essential for the theoretical initiation to the finite elements method. Other student populations who have followed a curriculum not specialised in mathematics – specially graduate and postgraduate students in Physics or in Mechanics and the Graduate Engineering Schools who are users of the mathematical tool at different degrees – may get recourse to Daniel Euvrard’s (5) book which was written in the 90’s and that offers a version of a course adapted to students who are unfamiliar with the tools for functional analysis. The superiority of those two manuals reflects the quality of the teachings of Numerical Analysis by Pierre Arnaud Raviart and subsequently by Daniel Euvrard at the Training and Research Unit in Mechanics of the Pierre and Marie Curie University. As far as this piece of work is concerned, its necessity and its core content have been greatly influenced by the strong interaction between components of the author’s teaching activities in mechanics, at graduate level, consisting of Numerical Methods applied to Mechanics and to the mechanics of deformable solids at the Pierre and Marie Curie University. Indeed, the author was motivated by the will to pursue the initiative set by the two authors mentioned above by contributing to a new balance between a selective specialist reading and one dedicated to “operational aspects while skimming over the mathematical aspects”, as stated by Daniel Euvrard ([5], p.198). The author’s training and awareness on all topics dealing with numerical analysis was greatly influenced by Professor Gérard Tronel, a specially active and passionate member of the team teaching numerical analysis at the Jacques Louis Lions laboratory of the Pierre and Marie Curie University (Paris VI). The author benefited from Professor Tronel’s significant educational methods and experience as a student and, later, as a colleague and friend, in bringing about the new balance offered in this book. The author’s warm thanks are conveyed to him for his contribution. Graduate students in Mechanics of the Pierre and Marie Curie University are the ones who have followed this novel presentation within the framework of unidimensional applications of the resistance of materials. The present work takes up these examples again and extends them to other applications. Having identified targeted tools for functional analysis, as exposed without any demonstration, the problems dealing with the existence, uniqueness and regularity of weak solutions and their equivalence with strong solutions have been examined through the display and use of the result of this identification. Following this perspective, the present work is composed of a Summary of Courses on finite elements in addition to Daniel Euvrard’s [5] work, and of various solutions demonstrating these techniques of functional analysis while, at the same time, tackling the construction of nodal equations characteristic of numerical implementation of the finite elements method. Moreover, a special emphasis has been laid on the presentation of the application of assembly techniques illustrated in the problems related to the Resistance of Materials. The author seizes this opportunity to pay tribute to the memory of Claude Kammoun who initiated him to these techniques within the framework of Resistance of Materials. Finally, this work would never have been published without Benoît Goyeau and Cédric Croizet’s proofreading of the different examination subjects at graduate level Mechanics that constitute a major part of this book. The author conveys his sincere thanks to both of them also to Dr. Arnaud Chauvière for his efficient advices in Latex Programmation.
Concurrency and Computation: Practice and Experience, 2014
We present a graphics processing unit (GPU) parallelization of the computation of the price of ex... more We present a graphics processing unit (GPU) parallelization of the computation of the price of exotic crosscurrency interest rate derivatives via a partial differential equation (PDE) approach. In particular, we focus on the GPU-based parallel pricing of long-dated foreign exchange (FX) interest rate hybrids, namely power reverse dual currency (PRDC) swaps with Bermudan cancelable features. We consider a three-factor pricing model with FX volatility skew, which results in a time-dependent parabolic PDE in three spatial dimensions. Finite difference methods on uniform grids are used for the spatial discretization of the PDE, and the alternating direction implicit (ADI) technique is employed for the time discretization. We then exploit the parallel architectural features of GPUs together with the Compute Unified Device Architecture framework to design and implement an efficient parallel algorithm for pricing PRDC swaps. Over each period of the tenor structure, we divide the pricing of a Bermudan cancelable PRDC swap into two independent pricing subproblems, each of which can efficiently be solved on a GPU via a parallelization of the ADI timestepping technique. Numerical results indicate that GPUs can provide significant increase in performance over CPUs when pricing PRDC swaps. An analysis of the impact of the FX skew on such derivatives is provided. PRDC swaps. The use of a local volatility model provides better modeling for the skewness of the FX rate and at the same time avoids introducing more stochastic factors into the model.
This paper presents the development of a workspace controller for a newly designed platform. The ... more This paper presents the development of a workspace controller for a newly designed platform. The platform is designed to manipulate endoscopic tools and is actuated by tendons to meet the small scale requirements in en-doscopy. The tendon actuation provides challenges to the controller design since the number of degrees of freedom equals the number of tendons. In typical tendon-driven systems, the number of tendons is greater than the number of degrees of freedom. This paper presents the kinematic and dynamic analysis of the manipulator and presents a workspace controller for the tendon driven system. Simulation as well as experimental results are presented for the controlled system. The results demonstrate the eec-tiveness of the controller in tracking a step response and a circular trajectory at 2.0Hz and greater. The device is similar to the Stewart platform and the basic design can be used in applications where the full range of motion of the Stewart platform is not required. Applications of the device range between targeting systems, snake-like robots, and endoscopy.
— During an automobile crash, some parts in the front of an automobile body will have plastic def... more — During an automobile crash, some parts in the front of an automobile body will have plastic deformation and absorb a lot of energy. Hence it becomes necessary to check the car structure for its crash ability so that safety is achieved together with fuel economy. A simple finite element (FE) model of a car is developed in ANSYS and it is solved for full frontal impact in ANSYS LS-DYNA explicit code. Computational simulations and various results are plotted and analyzed. There are various test configurations. We have limited our analysis to frontal impact with a rigid wall at a speed of 35 mph, corresponding to a NHTSA (National Highway Traffic Safety Administration) full frontal impact. It was noted that composite materials could be used more effectively for light-weightiness other than metallic materials without affecting the necessary impact energy absorbing capacity of the car body. Since composite materials and metallic materials absorb approximately the same energy during a car crash we conclude that composite materials can be used for light-weightiness in automobiles.
This book is dedicated to the use of the finite elements method for the approximation of equation... more This book is dedicated to the use of the finite elements method for the approximation of equations having partial derivatives. It resumes part of the curriculum leading to the certificate in “Numerical Methods forMechanics” taught by the author since the past twelve years as part of the graduate studies in Mechanics at the University of Pierre and Marie Curie (Paris VI). Numerical Analysis has undergone a spectacular development during these past forty years. It is most probably related to the boom in InformationTechnologywhich has literally invaded the planet and provided, de facto, calculation capacities undreamt of up to now. This mathematical knowledge field – Numerical Analysis – may be characterised as the “mathematic of mathematics” in the same line of thought as that of a “police of polices”. Indeed, as soon as a mathematical technology cannot be applied within the industrial applications due to operational inadequacy, numerical analysis takes over and finds the solution by identifying the best adapted approximation process. From there on, all other mathematical branches may be used to “force a passage” and to estimate a solution by often combining shrewdness and lucidity within a stringent mathematical framework. Numerical analysis is best and most often applied to the approximation of equations having partial derivatives as a major support to the modelling of real systems. Whether it be applications in physics or in mechanics, in economy, marketing or in the field of finance, the phenomenological translation of the system under study often leads to the resolution of equations having partial derivatives. This justifies the invention of numerous methods to solve such equations. The finite elements method, the finite volumes method, the singularity or integral method, the spectral methods and the variational finite differences method are some of the most popular methods. However, the finite elements are those that definitely and drastically changed the world of numerical approximation of equations having partial derivatives. Having an exceptional flexibility, the finite elements undoubtedly constitute the approximation method that is mostly used in solving mathematical models in engineering sciences. Considering the mathematical technicality required to apply finite elements, many authors specialised in numerical analysis, including Pierre Arnaud Raviart (8), presented the subject at higher level university teaching reserved to students who possess the mathematical prerequisites, particularly in function analysis, essential for the theoretical initiation to the finite elements method. Other student populations who have followed a curriculum not specialised in mathematics – specially graduate and postgraduate students in Physics or in Mechanics and the Graduate Engineering Schools who are users of the mathematical tool at different degrees – may get recourse to Daniel Euvrard’s (5) book which was written in the 90’s and that offers a version of a course adapted to students who are unfamiliar with the tools for functional analysis. The superiority of those two manuals reflects the quality of the teachings of Numerical Analysis by Pierre Arnaud Raviart and subsequently by Daniel Euvrard at the Training and Research Unit in Mechanics of the Pierre and Marie Curie University. As far as this piece of work is concerned, its necessity and its core content have been greatly influenced by the strong interaction between components of the author’s teaching activities in mechanics, at graduate level, consisting of Numerical Methods applied to Mechanics and to the mechanics of deformable solids at the Pierre and Marie Curie University. Indeed, the author was motivated by the will to pursue the initiative set by the two authors mentioned above by contributing to a new balance between a selective specialist reading and one dedicated to “operational aspects while skimming over the mathematical aspects”, as stated by Daniel Euvrard ([5], p.198). The author’s training and awareness on all topics dealing with numerical analysis was greatly influenced by Professor Gérard Tronel, a specially active and passionate member of the team teaching numerical analysis at the Jacques Louis Lions laboratory of the Pierre and Marie Curie University (Paris VI). The author benefited from Professor Tronel’s significant educational methods and experience as a student and, later, as a colleague and friend, in bringing about the new balance offered in this book. The author’s warm thanks are conveyed to him for his contribution. Graduate students in Mechanics of the Pierre and Marie Curie University are the ones who have followed this novel presentation within the framework of unidimensional applications of the resistance of materials. The present work takes up these examples again and extends them to other applications. Having identified targeted tools for functional analysis, as exposed without any demonstration, the problems dealing with the existence, uniqueness and regularity of weak solutions and their equivalence with strong solutions have been examined through the display and use of the result of this identification. Following this perspective, the present work is composed of a Summary of Courses on finite elements in addition to Daniel Euvrard’s [5] work, and of various solutions demonstrating these techniques of functional analysis while, at the same time, tackling the construction of nodal equations characteristic of numerical implementation of the finite elements method. Moreover, a special emphasis has been laid on the presentation of the application of assembly techniques illustrated in the problems related to the Resistance of Materials. The author seizes this opportunity to pay tribute to the memory of Claude Kammoun who initiated him to these techniques within the framework of Resistance of Materials. Finally, this work would never have been published without Benoît Goyeau and Cédric Croizet’s proofreading of the different examination subjects at graduate level Mechanics that constitute a major part of this book. The author conveys his sincere thanks to both of them also to Dr. Arnaud Chauvière for his efficient advices in Latex Programmation.
Uploads
Papers by Duy Hao Dang
Books by Duy Hao Dang
Numerical Analysis has undergone a spectacular development during these past forty years. It is most probably related to the boom in InformationTechnologywhich has literally invaded the planet and provided, de facto, calculation capacities undreamt
of up to now.
This mathematical knowledge field – Numerical Analysis – may be characterised as the “mathematic of mathematics” in the same line of thought as that of a “police of polices”.
Indeed, as soon as a mathematical technology cannot be applied within the industrial applications due to operational inadequacy, numerical analysis takes over and finds the solution by identifying the best adapted approximation process.
From there on, all other mathematical branches may be used to “force a passage” and to estimate a solution by often combining shrewdness and lucidity within a stringent mathematical framework.
Numerical analysis is best and most often applied to the approximation of equations having partial derivatives as a major support to the modelling of real systems.
Whether it be applications in physics or in mechanics, in economy, marketing or in the field of finance, the phenomenological translation of the system under study often leads to the resolution of equations having partial derivatives.
This justifies the invention of numerous methods to solve such equations. The finite elements method, the finite volumes method, the singularity or integral method, the spectral methods and the variational finite differences method are some of the most popular methods.
However, the finite elements are those that definitely and drastically changed the world of numerical approximation of equations having partial derivatives. Having an exceptional flexibility, the finite elements undoubtedly constitute the approximation method that is mostly used in solving mathematical models in engineering sciences.
Considering the mathematical technicality required to apply finite elements, many authors specialised in numerical analysis, including Pierre Arnaud Raviart (8), presented the subject at higher level university teaching reserved to students who possess the mathematical prerequisites, particularly in function analysis, essential for the theoretical initiation to the finite elements method.
Other student populations who have followed a curriculum not specialised in mathematics – specially graduate and postgraduate students in Physics or in Mechanics and the Graduate Engineering Schools who are users of the mathematical tool at different degrees – may get recourse to Daniel Euvrard’s (5) book which was written in the 90’s and that offers a version of a course adapted to students who are unfamiliar with the tools for functional analysis.
The superiority of those two manuals reflects the quality of the teachings of Numerical
Analysis by Pierre Arnaud Raviart and subsequently by Daniel Euvrard at the Training and Research Unit in Mechanics of the Pierre and Marie Curie University.
As far as this piece of work is concerned, its necessity and its core content have been greatly influenced by the strong interaction between components of the author’s teaching activities in mechanics, at graduate level, consisting of Numerical Methods applied to Mechanics and to the mechanics of deformable solids at the Pierre and Marie Curie University.
Indeed, the author was motivated by the will to pursue the initiative set by the two authors mentioned above by contributing to a new balance between a selective specialist reading and one dedicated to “operational aspects while skimming over the mathematical aspects”, as stated by Daniel Euvrard ([5], p.198).
The author’s training and awareness on all topics dealing with numerical analysis was greatly influenced by Professor Gérard Tronel, a specially active and passionate member of the team teaching numerical analysis at the Jacques Louis Lions laboratory of the Pierre and Marie Curie University (Paris VI).
The author benefited from Professor Tronel’s significant educational methods and experience as a student and, later, as a colleague and friend, in bringing about the new balance offered in this book.
The author’s warm thanks are conveyed to him for his contribution.
Graduate students in Mechanics of the Pierre and Marie Curie University are the ones who have followed this novel presentation within the framework of unidimensional applications of the resistance of materials.
The present work takes up these examples again and extends them to other applications.
Having identified targeted tools for functional analysis, as exposed without any demonstration, the problems dealing with the existence, uniqueness and regularity of weak solutions and their equivalence with strong solutions have been examined through the display and use of the result of this identification.
Following this perspective, the present work is composed of a Summary of Courses on finite elements in addition to Daniel Euvrard’s [5] work, and of various solutions demonstrating these techniques of functional analysis while, at the same time, tackling the construction of nodal equations characteristic of numerical implementation of the finite elements method.
Moreover, a special emphasis has been laid on the presentation of the application of assembly techniques illustrated in the problems related to the Resistance of Materials.
The author seizes this opportunity to pay tribute to the memory of Claude Kammoun who initiated him to these techniques within the framework of Resistance of Materials.
Finally, this work would never have been published without Benoît Goyeau and Cédric Croizet’s proofreading of the different examination subjects at graduate level Mechanics that constitute a major part of this book. The author conveys his sincere thanks to both of them also to Dr. Arnaud Chauvière for his efficient advices in Latex Programmation.
Numerical Analysis has undergone a spectacular development during these past forty years. It is most probably related to the boom in InformationTechnologywhich has literally invaded the planet and provided, de facto, calculation capacities undreamt
of up to now.
This mathematical knowledge field – Numerical Analysis – may be characterised as the “mathematic of mathematics” in the same line of thought as that of a “police of polices”.
Indeed, as soon as a mathematical technology cannot be applied within the industrial applications due to operational inadequacy, numerical analysis takes over and finds the solution by identifying the best adapted approximation process.
From there on, all other mathematical branches may be used to “force a passage” and to estimate a solution by often combining shrewdness and lucidity within a stringent mathematical framework.
Numerical analysis is best and most often applied to the approximation of equations having partial derivatives as a major support to the modelling of real systems.
Whether it be applications in physics or in mechanics, in economy, marketing or in the field of finance, the phenomenological translation of the system under study often leads to the resolution of equations having partial derivatives.
This justifies the invention of numerous methods to solve such equations. The finite elements method, the finite volumes method, the singularity or integral method, the spectral methods and the variational finite differences method are some of the most popular methods.
However, the finite elements are those that definitely and drastically changed the world of numerical approximation of equations having partial derivatives. Having an exceptional flexibility, the finite elements undoubtedly constitute the approximation method that is mostly used in solving mathematical models in engineering sciences.
Considering the mathematical technicality required to apply finite elements, many authors specialised in numerical analysis, including Pierre Arnaud Raviart (8), presented the subject at higher level university teaching reserved to students who possess the mathematical prerequisites, particularly in function analysis, essential for the theoretical initiation to the finite elements method.
Other student populations who have followed a curriculum not specialised in mathematics – specially graduate and postgraduate students in Physics or in Mechanics and the Graduate Engineering Schools who are users of the mathematical tool at different degrees – may get recourse to Daniel Euvrard’s (5) book which was written in the 90’s and that offers a version of a course adapted to students who are unfamiliar with the tools for functional analysis.
The superiority of those two manuals reflects the quality of the teachings of Numerical
Analysis by Pierre Arnaud Raviart and subsequently by Daniel Euvrard at the Training and Research Unit in Mechanics of the Pierre and Marie Curie University.
As far as this piece of work is concerned, its necessity and its core content have been greatly influenced by the strong interaction between components of the author’s teaching activities in mechanics, at graduate level, consisting of Numerical Methods applied to Mechanics and to the mechanics of deformable solids at the Pierre and Marie Curie University.
Indeed, the author was motivated by the will to pursue the initiative set by the two authors mentioned above by contributing to a new balance between a selective specialist reading and one dedicated to “operational aspects while skimming over the mathematical aspects”, as stated by Daniel Euvrard ([5], p.198).
The author’s training and awareness on all topics dealing with numerical analysis was greatly influenced by Professor Gérard Tronel, a specially active and passionate member of the team teaching numerical analysis at the Jacques Louis Lions laboratory of the Pierre and Marie Curie University (Paris VI).
The author benefited from Professor Tronel’s significant educational methods and experience as a student and, later, as a colleague and friend, in bringing about the new balance offered in this book.
The author’s warm thanks are conveyed to him for his contribution.
Graduate students in Mechanics of the Pierre and Marie Curie University are the ones who have followed this novel presentation within the framework of unidimensional applications of the resistance of materials.
The present work takes up these examples again and extends them to other applications.
Having identified targeted tools for functional analysis, as exposed without any demonstration, the problems dealing with the existence, uniqueness and regularity of weak solutions and their equivalence with strong solutions have been examined through the display and use of the result of this identification.
Following this perspective, the present work is composed of a Summary of Courses on finite elements in addition to Daniel Euvrard’s [5] work, and of various solutions demonstrating these techniques of functional analysis while, at the same time, tackling the construction of nodal equations characteristic of numerical implementation of the finite elements method.
Moreover, a special emphasis has been laid on the presentation of the application of assembly techniques illustrated in the problems related to the Resistance of Materials.
The author seizes this opportunity to pay tribute to the memory of Claude Kammoun who initiated him to these techniques within the framework of Resistance of Materials.
Finally, this work would never have been published without Benoît Goyeau and Cédric Croizet’s proofreading of the different examination subjects at graduate level Mechanics that constitute a major part of this book. The author conveys his sincere thanks to both of them also to Dr. Arnaud Chauvière for his efficient advices in Latex Programmation.