1,317 research outputs found
Transient Analysis of High-Speed Channels via Newton-GMRES Waveform Relaxation
This paper presents a technique for the numerical simulation of coupled high-speed channels terminated by arbitrary nonlinear drivers and receivers. The method builds on a number of existing techniques. A Delayed-Rational Macromodel is used to describe the channel in compact form, and a general Waveform Relaxation framework is used to cast the solution as an iterative process that refines initial estimates of transient scattering waves at the channel ports. Since a plain Waveform Relaxation approach is not able to guarantee convergence, we turn to a more general class of nonlinear algebraic solvers based on a combination of the Newton method with a Generalized Minimal Residual iteration, where the Waveform Relaxation equations act as a preconditioner. The convergence of this scheme can be proved in the general case. Numerical examples show that very few iterations are indeed required even for strongly nonlinear termination
A multidomain spectral method for solving elliptic equations
We present a new solver for coupled nonlinear elliptic partial differential
equations (PDEs). The solver is based on pseudo-spectral collocation with
domain decomposition and can handle one- to three-dimensional problems. It has
three distinct features. First, the combined problem of solving the PDE,
satisfying the boundary conditions, and matching between different subdomains
is cast into one set of equations readily accessible to standard linear and
nonlinear solvers. Second, touching as well as overlapping subdomains are
supported; both rectangular blocks with Chebyshev basis functions as well as
spherical shells with an expansion in spherical harmonics are implemented.
Third, the code is very flexible: The domain decomposition as well as the
distribution of collocation points in each domain can be chosen at run time,
and the solver is easily adaptable to new PDEs. The code has been used to solve
the equations of the initial value problem of general relativity and should be
useful in many other problems. We compare the new method to finite difference
codes and find it superior in both runtime and accuracy, at least for the
smooth problems considered here.Comment: 31 pages, 8 figure
High performance implementation of MPC schemes for fast systems
In recent years, the number of applications of model predictive control (MPC) is rapidly
increasing due to the better control performance that it provides in comparison to
traditional control methods. However, the main limitation of MPC is the computational
e ort required for the online solution of an optimization problem. This shortcoming
restricts the use of MPC for real-time control of dynamic systems with high sampling
rates. This thesis aims to overcome this limitation by implementing high-performance
MPC solvers for real-time control of fast systems. Hence, one of the objectives of this
work is to take the advantage of the particular mathematical structures that MPC
schemes exhibit and use parallel computing to improve the computational e ciency.
Firstly, this thesis focuses on implementing e cient parallel solvers for linear MPC
(LMPC) problems, which are described by block-structured quadratic programming
(QP) problems. Speci cally, three parallel solvers are implemented: a primal-dual
interior-point method with Schur-complement decomposition, a quasi-Newton method
for solving the dual problem, and the operator splitting method based on the alternating
direction method of multipliers (ADMM). The implementation of all these solvers is
based on C++. The software package Eigen is used to implement the linear algebra
operations. The Open Message Passing Interface (Open MPI) library is used for the
communication between processors. Four case-studies are presented to demonstrate the
potential of the implementation. Hence, the implemented solvers have shown high
performance for tackling large-scale LMPC problems by providing the solutions in
computation times below milliseconds.
Secondly, the thesis addresses the solution of nonlinear MPC (NMPC) problems, which
are described by general optimal control problems (OCPs). More precisely,
implementations are done for the combined multiple-shooting and collocation (CMSC)
method using a parallelization scheme. The CMSC method transforms the OCP into a
nonlinear optimization problem (NLP) and de nes a set of underlying sub-problems for
computing the sensitivities and discretized state values within the NLP solver. These
underlying sub-problems are decoupled on the variables and thus, are solved in parallel.
For the implementation, the software package IPOPT is used to solve the resulting NLP
problems. The parallel solution of the sub-problems is performed based on MPI and
Eigen. The computational performance of the parallel CMSC solver is tested using case
studies for both OCPs and NMPC showing very promising results.
Finally, applications to autonomous navigation for the SUMMIT robot are presented.
Specially, reference tracking and obstacle avoidance problems are addressed using an
NMPC approach. Both simulation and experimental results are presented and compared
to a previous work on the SUMMIT, showing a much better computational e ciency
and control performance.Tesi
A new nonlocal thermodynamical equilibrium radiative transfer method for cool stars
Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE)
radiative transfer equation usually relies on stationary iterative methods,
which may falsely converge in some cases. Furthermore, these methods are often
unable to handle large-scale systems, such as molecular spectra emerging from,
for example, cool stellar atmospheres.
Aims: Our objective is to develop a new method, which aims to circumvent
these problems, using nonstationary numerical techniques and taking advantage
of parallel computers.
Methods: The technique we develop may be seen as a generalization of the
coupled escape probability method. It solves the statistical equilibrium
equations in all layers of a discretized model simultaneously. The numerical
scheme adopted is based on the generalized minimum residual method.
Result:. The code has already been applied to the special case of the water
spectrum in a red supergiant stellar atmosphere. This demonstrates the fast
convergence of this method, and opens the way to a wide variety of
astrophysical problems.Comment: 13 pages, 9 figure
Efficient parallelization strategy for real-time FE simulations
This paper introduces an efficient and generic framework for finite-element
simulations under an implicit time integration scheme. Being compatible with
generic constitutive models, a fast matrix assembly method exploits the fact
that system matrices are created in a deterministic way as long as the mesh
topology remains constant. Using the sparsity pattern of the assembled system
brings about significant optimizations on the assembly stage. As a result,
developed techniques of GPU-based parallelization can be directly applied with
the assembled system. Moreover, an asynchronous Cholesky precondition scheme is
used to improve the convergence of the system solver. On this basis, a
GPU-based Cholesky preconditioner is developed, significantly reducing the data
transfer between the CPU/GPU during the solving stage. We evaluate the
performance of our method with different mesh elements and hyperelastic models
and compare it with typical approaches on the CPU and the GPU
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