The adjoint reversal of long evolutionary calculations (e.g. loops), where each iteration depends on the output of the previous iteration, is a common occurrence in computationalengineering (e.g. computational fluid ...
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The efficient computation of Jacobians represents a fundamental challenge in computational science and engineering. Large-scale modular numerical simulation programs can be regarded as sequences of evaluations of in o...
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The implicit Euler method integrates systems of ordinary differential equations dx dt = G(t, x(t)) with differentiable right-hand side G : R × Rn → Rn from an initial state x = x(0) ∈ Rn to a target time t ∈ R...
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MSC Codes 00-02We use Algorithmic Differentiation (AD) [1] to implement type-generic tangent and adjoint versions of (formula presented) in C++. We run an instantiation for char-arithmetic and we print the gradient at...
We want to obtain derivatives in discontinuous program code, where default Algorithmic Differentiation may not perform well. Specifically, we consider discontinuities induced by control flow statements, where meaningf...
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A modification of Newton’s method for solving systems of n nonlinear equations is presented. The new matrix-free method relies on a given decomposition of the invertible Jacobian of the residual into invertible spars...
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All known elimination techniques for (first-order) algorithmic differentiation (AD) rely on Jacobians to be given for a set of relevant elemental functions. Realistically, elemental tangents and adjoints are given ins...
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We are considering differential-algebraic equations with embedded optimization criteria (DAEOs) in which the embedded optimization problem is solved by global optimization. This actually leads to differential inclusio...
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Adjoint algorithmic differentiation by operator and function overloading is based on the interpretation of directed acyclic graphs resulting from evaluations of numerical simulation programs. The size of the computer ...
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We describe how to deploy interval derivatives up to second order in the context of unconstrained global optimization with a branch and bound method. For computing these derivatives we combine the Boost interval libra...
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