相关论文: New Optimization Methods for Converging Perturbati…
In this paper we analyze the relaxed form of a shape optimization problem with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D \hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the term $f$ is…
We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant g_B for which we possess a finite number L of expansion coefficients plus two more informations: The…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
We discuss the weak coupling expansion of a one plaquette SU(2) lattice gauge theory. We show that the conventional perturbative series for the partition function has a zero radius of convergence and is asymptotic. The average plaquette is…
PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty…
Some methods for the convergence acceleration of the M{\o}ller-Plesset perturbation series for the correlation energy are discussed. The order-by-order summation is less effective than the Feenberg series. The latter is obtained by…
A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
We present a Monte Carlo study of the one-component $\phi^4$ model on the cubic lattice in three dimensions. Leading order scaling corrections are studied using the finite size scaling method. We compute the corrections to scaling exponent…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…
The predictive power of perturbative QCD (pQCD) depends on two important issues: (1) how to eliminate the renormalization scheme-and-scale ambiguities at fixed order, and (2) how to reliably estimate the contributions of unknown…
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
We introduce a geometric and operator-theoretic formalism viewing optimization algorithms as discrete connections on a space of update operators. Each iterative method is encoded by two coupled channels-drift and diffusion-whose algebraic…
We investigate the strong coupling problem in modified teleparallel gravity theories using the effective field theory (EFT) approach, demonstrating that it is possible to shift the emergence of new degrees of freedom (DoFs) to lower orders…
Perturbative QCD corrections to hadronic $\tau$ decays and $e^+e^-$ annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong…