We present a generic approach to transforming one-sided MPI communication in the context of adjoint code. The adjoint allows us to compute gradients of multivariate function implementations at a computational cost tha...
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OpenMP and MPI are typically used in combination to implement distributed shared memory parallelization schemes for numerical simulations on hybrid systems. The performance of said numerical simulations is frequently ...
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This case study in Algorithmic Differentiation (AD) discusses the semi-automatic generation of an adjoint simulation code in the context of an inverse atmospheric remote sensing problem. In-depth structural and perfor...
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Algorithmic differentiation is a growing area of research that is concerned with the accuracy and efficient evaluation of derivatives for numerical functions defined by computer programs. In this paper, algorithmic di...
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Algorithmic differentiation is a growing area of research that is concerned with the accuracy and efficient evaluation of derivatives for numerical functions defined by computer programs. In this paper, algorithmic differentiation by overloading is introduced and applied to the linear solver F07AEF of the NAG library. As a case study and for the verification purpose, its result is used to compute the sensitivity of the Newton method in solving a nonlinear system of equation generated by a minimum problem. The function chosen for the case study is Extended Rosenbrock function.
An essential performance and correctness factor in numerical simulation and optimization is access to exact derivative information. Adjoint derivative models are particularly useful if a function’s number of inputs f...
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An essential performance and correctness factor in numerical simulation and optimization is access to exact derivative information. Adjoint derivative models are particularly useful if a function’s number of inputs far exceeds the number of outputs. The propagation of adjoints requires the data flow to be reversed, implying the reversal of all communication in programs that use message-passing. This paper presents recent advances made in developing the adjoint MPI library AMPI. The described proof of concept aims to serve as the basis for coupling other overloading AD tools with AMPI. We illustrate its use in the context of a specific overloading tool for algorithmic differentiation (AD) for C++ programs. A simplified but representative application problem is discussed as a case study.
Goal oriented dual weight error estimation has been used in context of computational fluid dynamics for several years. The adaptation of this method to geophysical models is the subject of this paper. A differentiatio...
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Goal oriented dual weight error estimation has been used in context of computational fluid dynamics for several years. The adaptation of this method to geophysical models is the subject of this paper. A differentiation-enabled prototype of the NAG Fortran compiler is used to generate a discrete adjoint version of such a geophysical model and allows to compute the required goal sensitivities. Numerical results are presented for a shallow water configuration of the Icosahedral Non-hydrostatic General Circulation Model (ICON). A special treatment of the underlying linear solver is discussed yielding improved scalability of this approach and a significant reduction in memory consumption and runtime.
We describe the use of first- and second-order tangent-linear and adjoint models of the residual of linear-implicit autonomous differential algebraic systems in the context of an extrapolated Euler scheme. The derivat...
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We describe the use of first- and second-order tangent-linear and adjoint models of the residual of linear-implicit autonomous differential algebraic systems in the context of an extrapolated Euler scheme. The derivative code compiler dcc is applied to a C-implementation of the residual to get first derivative code. Second-(and higher-)order derivative models are obtained by reapplication of dcc to its own output. The resulting solver serves as a first proof of concept of a new platform for source-level manipulation of mathematical models that is currently under development at RWTH Aachen University.
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