Search

An efficient improved spectrum integral method (ISIM) is proposed to accelerate the scattering simulation of cuboid object by method of moment (MoM) in multiplanar layered medium (LM). The layered medium Green’s functions (LMGFs) are studied and decomposed into transmission and reflection terms, which hold the translational invariance and reverse translational invariance, respectively. By virtue of the (reverse) translational invariance of LMGF from the uniform square grids on the surface of the cuboid object, most of the coupling between the expanding basis functions and the testing basis functions can be represented by two kinds of submatrices, i.e., the Toeplitz matrix when transmission term is involved, and the conjugate Toeplitz matrix when reflection term is involved. Moreover, the submatrix coupling the expanding/testing basis functions defined on the edges with those defined on the parallel surfaces/edges is also extended to the (conjugate) Toeplitz matrixes. This will significantly alleviate the heavy computation and memory burden from the conventional SIM. With the improved operations on the basis functions associated with the edges of the cuboid object, the proposed ISIM in LM can reach the computational complexity as low as ${O}$ (${N} ^{1.5}$ log(N)) in the matrix vector production, while the computational complexity of matrix filling and the memory requirement are both ${O}$ (${N}^{1.5}$). Moreover, compared with conventional SIM, both theoretical analysis and numerical results demonstrate that the memory requirement and matrix filling time are dramatically decreased. [ABSTRACT FROM AUTHOR]

Learning discriminative and invariant feature representation is the key to visual image categorization. In this article, we propose a novel invariant deep compressible covariance pooling (IDCCP) to solve nuisance variations in aerial scene categorization. We consider transforming the input image according to a finite transformation group that consists of multiple confounding orthogonal matrices, such as the D4 group. Then, we adopt a Siamese-style network to transfer the group structure to the representation space, where we can derive a trivial representation that is invariant under the group action. The linear classifier trained with trivial representation will also be possessed with invariance. To further improve the discriminative power of representation, we extend the representation to the tensor space while imposing orthogonal constraints on the transformation matrix to effectively reduce feature dimensions. We conduct extensive experiments on the publicly released aerial scene image data sets and demonstrate the superiority of this method compared with state-of-the-art methods. In particular, with using ResNet architecture, our IDCCP model can reduce the dimension of the tensor representation by about 98% without sacrificing accuracy (i.e., < 0.5%). [ABSTRACT FROM AUTHOR]

A novel hydraulic fracture scattering simulation method in the hydrocarbon diagnosis is developed in this article. The traditional thin dielectric structure-based surface integral equation (TDS-SIE) is adopted for accurate and stable fracture scattering analysis. To improve the low simulation efficiency of conventional TDS-SIE, a higher order TDS-SIE (HO-TDS-SIE) is developed in this article. The junction vector bases are defined to extend TDS-SIE for the branched fractures. Moreover, the matrix normalization method is adopted to improve the conditioning of impedance matrices and accelerate the convergence rate. The excellent performance of this new HO-TDS-SIE solver for complex hydraulic fracture and network is validated by numerical experiments. To best of our knowledge, this is the first time to extend TDS-SIE into higher order scheme for accurate fracture scattering simulation. [ABSTRACT FROM AUTHOR]

This paper presents a novel accurate and stable current and charge integral equation (CCIE) solver for the low-frequency scattering of penetrable objects in layered medium (LM). To the best of our knowledge, this is the first time to extend CCIE into LM simulations at low frequency. In order to integrate the matrix-friendly LM Green’s functions (LMGFs) into CCIE, we have rederived them to define new quasi-vector/scalar potentials, which are able to annihilate the frequency singularity in the original LMGFs. Moreover, an effective preconditioner is adopted to improve the conditioning of impedance matrices. In comparison with other perconditioners, this method performs much better. The excellent performance of this new CCIE solver is then demonstrated by numerical experiments. [ABSTRACT FROM AUTHOR]

We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave propagation in viscous media. To include the attenuation and dispersion due to the quality factor in time domain, several sets of auxiliary ordinary differential equations (AODEs) are added. Unlike the conventional auxiliary partial differential equation-based algorithm, this new method is highly parallel with its lossless counterpart, thus requiring much less time and storage consumption. Another superior property of the AODE-based DG method is that a novel exact Riemann solver can be derived, which allows heterogeneous viscoelastic coupling, in addition to accurate coupling with purely elastic media and fluid. Furthermore, thanks to the nonconformal-mesh technique, adaptive hp-refinement and flexible memory allocation for the auxiliary variables are achieved. Numerical results demonstrate the efficiency and accuracy of our method. [ABSTRACT FROM PUBLISHER]

A novel hybrid method is developed for the flexible and accurate electromagnetic simulation of penetrable objects in a layered medium (LM). In this method, the original complex simulation domain is first divided into several subdomains, following the spirit of divide-and-conquer. Each subdomain is then meshed and solved independently, where nonconformal mesh is inevitable. The Riemann type transmission condition is utilized at the interfaces of each subdomain to correctly exchange information so that the solutions of all subdomains converge rapidly to the real solution of the original problem. More specifically, in our method, the surface integral equation (SIE) combined with the LM Green’s functions (LMGFs) is adopted for the boundary subdomain, while the finite-element method (FEM) and the spectral element method (SEM) are employed for all the other interior dielectric subdomains. The SIE with LMGFs truncates the simulation domain tightly within the object itself, which drastically decreases the number of unknowns. The interior subdomains are modeled by either FEM or SEM, depending on the geometry and material property of each subdomain. To further enhance the simulation capability, higher order approaches are adopted for all the subdomain solvers in this hybrid method. Several numerical examples are demonstrated, where a high convergence and accuracy of this method is observed. This paper will serve as an efficient and flexible simulation tool for the applications of geophysical exploration. [ABSTRACT FROM PUBLISHER]