Software tools for analysis and synthesis of stochastic systems with high availability (XII)

The article proceeds the thematic cycle dedicated to analysis and synthesis for mean square criteria software tools for vector nonstationary (e.g. shock disturbances) linear stochastic systems with high availability (StSHA). Methodological support is based on Haar wavelet expansions (WLE) and wavelet canonical expansions (WLCE). Sect.1 is dedicated to problems statements. General basic algorithm is given in Sect. 2. Algorithms for StSHA with linear parameters and additive noises based on WLE and WLCE are described in Sect.3. Software tools in MATLAB are considered in Sect. 4. For typical shock disturbances bank of algorithms is developed. Complex of examples is given in Sect.5. Some generalizations are presented.

Wavelet-Based Subspace Regularization for Solving Highly Nonlinear Inverse Scattering Problems with Contraction Integral Equation

A wavelet transform twofold subspace-based optimization method (WT-TSOM) is proposed to solve the highly nonlinear inverse scattering problems with contraction integral equation for inversion (CIE-I). While the CIE-I is able to suppress the multiple scattering effects within inversion (without compromising the accuracy of the physics), proper regularization is needed. In this paper, we investigate a new type subspace regularization technique based on wavelet expansions for the induced currents. We found that the bior3.5 wavelet is a good choice to stabilize the inversions with the CIE-I model and in the meanwhile it also can rectify the contrast profile. Numerical tests against both synthetic and experimental data show that WT-TSOM is a promising regularization technique for inversion with CIE-I.

An adaptive space-time shock capturing method with high order wavelet bases for the system of shallow water equations

PurposeThis paper aims to propose an adaptive method for the numerical solution of the shallow water equations (SWEs). The authors provide an arbitrary high-order method using high-order spline wavelets. Furthermore, they use a non-linear shock capturing (SC) diffusion which removes the necessity of post-processing.Design/methodology/approachThe authors use a space-time weak formulation of SWEs which exploits continuous Galerkin (cG) in space and discontinuous Galerkin (dG) in time allowing time stepping, also known as cGdG. Such formulations along with SC term have recently been proved to ensure the stability of fully discrete schemes without scarifying the accuracy. However, the resulting scheme is expensive in terms of number of degrees of freedom (DoFs). By using natural adaptivity of wavelet expansions, the authors devise an adaptive algorithm to reduce the number of DoFs.FindingsThe proposed algorithm uses DoFs in a dynamic way to capture the shocks in all time steps while keeping the representation of approximate solution sparse. The performance of the proposed scheme is shown through some numerical examples.Originality/valueAn incorporation of wavelets for adaptivity in space-time weak formulations applied for SWEs is proposed.