Symmetric linear multistep integrator #1154
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eggrobin
reviewed
Nov 27, 2016
| double denominator; | ||
| }; | ||
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| template <typename Position, int order_> |
| // Definition of an Adams-Moulton integrator used for computing velocities. | ||
| template<int order_> | ||
| struct AdamsMoulton { | ||
| static int const order = order_; |
| // The velocity is evaluated for a single step, and for a method of order | ||
| // n a single step has order n + 1. This declaration gives us the velocity | ||
| // with order |order_|. | ||
| static int const velocity_order_ = order_ - 1; |
| using ODE = SpecialSecondOrderDifferentialEquation<Position>; | ||
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| SymmetricLinearMultistepIntegrator( | ||
| serialization::FixedStepSizeIntegrator::Kind const kind, |
| AdamsMoulton<velocity_order_> const& velocity_integrator, | ||
| FixedVector<double, half_order_> const& ɑ, | ||
| FixedVector<double, half_order_> const& β_numerator, | ||
| double const β_denominator); |
| IntegrationInstance::AppendState<ODE> append_state, | ||
| Time const& step) const; | ||
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| static int const order = order_; |
| // The latter has a general formula for the coefficients and was used to | ||
| // compute the high-order integrators. | ||
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| AdamsMoulton<1> const& AdamsMoultonOrder1() { |
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There is a unique Adams-Moulton method of order k. Make this a function template and write specializations. Moreover, I'd like AdamsMoulton to be in a separate file: even though we do not implement the actual Adams-Moulton method, it is a different thing which we happen to reuse for the symmetric linear multistep integrator.
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| // Fill the new step. We skip the division by ɑk as it is equal to 1.0. | ||
| double const ɑk = ɑ_[0]; | ||
| CHECK_EQ(ɑk, 1.0); |
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Do we have to do this in a loop? it seems like it should be done at construction.
| CHECK_EQ(ɑk, 1.0); | ||
| typename ODE::SystemState& system_state = down_cast_instance->current_state; | ||
| std::vector<Position> positions; | ||
| positions.reserve(dimension); |
| @@ -32,6 +32,8 @@ class FixedVector { | |||
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| operator std::vector<Scalar>() const; | |||
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| static int const size = size_; | |||
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