Subdomain Interface Research Articles

The generalized finite difference method for long-time transient heat conduction in 3D anisotropic composite materials

• Developing a combined KDC-GFDM scheme for long-time dynamic simulations. • Proposing a domain-decomposition GFDM for 3D anisotropic composite materials. • Introducing a new distance criterion for the adaptive selection of nodes in the GFDM. • Extremely large time step-sizes can be used in temporal discretization . In this paper we investigate the application of the generalized finite difference method (GFDM) to three-dimensional (3D) transient heat conduction in anisotropic composite (layered) materials. In our computations, the Krylov deferred correction (KDC) method, a pseudo-spectral type time-marching technique, is introduced to perform temporal discretization in time-domain. The KDC method allows discretizing the temporal direction using relatively large time-steps, making the method very promising for dynamic simulations, particularly when high precision is desired. A multi-domain GFDM scheme is also employed where the composite material considered is decomposed into several sub-domains and, in each sub-domain, the solution is approximated by using the GFDM expansion. On the sub-domain interface, compatibility of temperatures and normal heat fluxes is imposed. The method is tested on several benchmark numerical examples and its relative merits and disadvantages are discussed.

Asymptotic analysis of optimized Schwarz methods for maxwell’s equations with discontinuous coefficients

Discretized time harmonic Maxwell’s equations are hard to solve by iterative methods, and the best currently available methods are based on domain decomposition and optimized transmission conditions. Optimized Schwarz methods were the first ones to use such transmission conditions, and this approach turned out to be so fundamentally important that it has been rediscovered over the last years under the name sweeping preconditioners, source transfer, single layer potential method and the method of polarized traces. We show here how one can optimize transmission conditions to take benefit from the jumps in the coefficients of the problem, when they are aligned with the subdomain interface, and obtain methods which converge for two subdomains in certain situations independently of the mesh size, which would not be possible without jumps in the coefficients.

A Novel Hybrid Boundary-Type Meshless Method for Solving Heat Conduction Problems in Layered Materials

In this article, we propose a novel meshless method for solving two-dimensional stationary heat conduction problems in layered materials. The proposed method is a recently developed boundary-type meshless method which combines the collocation scheme from the method of fundamental solutions (MFS) with the collocation Trefftz method (CTM) to improve the applicability of the method for solving boundary value problems. Particular non-singular basis functions from cylindrical harmonics are adopted in which the numerical approximation is based on the superposition principle using the non-singular basis functions expressed in terms of many source points. For the modeling of multi-layer composite materials, we adopted the domain decomposition method (DDM), which splits the domain into smaller subdomains. The continuity of the flux and the temperature has to be satisfied at the interface of subdomains for the problem. The validity of the proposed method is investigated for several test problems. Numerical applications were also carried out. Comparison of the proposed method with other meshless methods showed that it is highly accurate and computationally efficient for modeling heat conduction problems, especially in heterogeneous multi-layer composite materials.

Mechanism of Selective Enzyme Inhibition through Uncompetitive Regulation of an Allosteric Agonist.

Classical uncompetitive inhibitors are potent pharmacological modulators of enzyme function. Since they selectively target enzyme-substrate complexes (E:S), their inhibitory potency is amplified by increasing substrate concentrations. Recently, an unconventional uncompetitive inhibitor, called CE3F4R, was discovered for the exchange protein activated by cAMP isoform 1 (EPAC1). Unlike conventional uncompetitive inhibitors, CE3F4R is uncompetitive with respect to an allosteric effector, cAMP, as opposed to the substrate (i.e., CE3F4R targets the E:cAMP rather than the E:S complex). However, the mechanism of CE3F4R as an uncompetitive inhibitor is currently unknown. Here, we elucidate the mechanism of CE3F4R's action using NMR spectroscopy. Due to limited solubility and line broadening, which pose major challenges for traditional structural determination approaches, we resorted to a combination of protein- and ligand-based NMR experiments to comparatively analyze EPAC mutations, inhibitor analogs, and cyclic nucleotide derivatives that trap EPAC at different stages of activation. We discovered that CE3F4R binds within the EPAC cAMP-binding domain (CBD) at a subdomain interface distinct from the cAMP binding site, acting as a wedge that stabilizes a cAMP-bound mixed-intermediate. The mixed-intermediate includes attributes of both the apo/inactive and cAMP-bound/active states. In particular, the intermediate targeted by CE3F4R traps a CBD's hinge helix in its inactive conformation, locking EPAC into a closed domain topology that restricts substrate access to the catalytic domain. The proposed mechanism of action also explains the isoform selectivity of CE3F4R in terms of a single EPAC1 versus EPAC2 amino acid difference that destabilizes the active conformation of the hinge helix.

Domain-decomposition generalized finite difference method for stress analysis in multi-layered elastic materials

The generalized finite difference method (GFDM) is a relatively new meshless method for the numerical solution of certain boundary value problems. The method uses the Taylor series expansions and the moving least squares approximation to derive explicit formulae for the required partial derivatives of unknown variables. In this paper, we document the first attempt to apply the GFDM for the numerical solution of two-dimensional (2D) multi-layered elastic problems. A multi-domain GFDM scheme is proposed to model the composite (layered) elastic materials. The composite material considered is decomposed into several sub-domains and, in each sub-domain, the solution is approximated by using the GFDM-type expansion. On the subdomain interface, compatibility of displacements and equilibrium of tractions are imposed. Preliminary numerical experiments show that the introduced multi-domain GFDM is very promising for accurate and efficient numerical simulations of multi-layered materials.

A mixed parallel strategy for the solution of coupled multi-scale problems at finite strains

A mixed parallel strategy for the solution of homogenization-based multi-scale constitutive problems undergoing finite strains is proposed. The approach aims to reduce the computational time and memory requirements of non-linear coupled simulations that use finite element discretization at both scales (FE $$^2$$ ). In the first level of the algorithm, a non-conforming domain decomposition technique, based on the FETI method combined with a mortar discretization at the interface of macroscopic subdomains, is employed. A master–slave scheme, which distributes tasks by macroscopic element and adopts dynamic scheduling, is then used for each macroscopic subdomain composing the second level of the algorithm. This strategy allows the parallelization of FE $$^2$$ simulations in computers with either shared memory or distributed memory architectures. The proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the Newton–Raphson scheme. Several examples are presented to demonstrate the robustness and efficiency of the proposed parallel strategy.

A parallel finite volume scheme preserving positivity for diffusion equation on distorted meshes

Parallel domain decomposition methods are natural and efficient for solving the implicity schemes of diffusion equations on massive parallel computer systems. A finite volume scheme preserving positivity is essential for getting accurate numerical solutions of diffusion equations and ensuring the numerical solutions with physical meaning. We call their combination as a parallel finite volume scheme preserving positivity, and construct such a scheme for diffusion equation on distorted meshes. The basic procedure of constructing the parallel finite volume scheme is based on the domain decomposition method with the prediction‐correction technique at the interface of subdomains: First, we predict the values on each inner interface of subdomains partitioned by the domain decomposition. Second, we compute the values in each subdomain using a finite volume scheme preserving positivity. Third, we correct the values on each inner interface using the finite volume scheme preserving positivity. The resulting scheme has intrinsic parallelism, and needs only local communication among neighboring processors. Numerical results are presented to show the performance of our schemes, such as accuracy, stability, positivity, and parallel speedup.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2159–2178, 2017

О построении двумерных локально-модифицированных квазиструктурированных сеток и решении на них краевых задач в областях с криволинейной границей последовательных наблюдений

New approaches to local modification quasistructured grids, which allow to track the inhomogeneous boundary value problems in the computational domain and adaptable to curved boundaries, as well as easy to use and does not require the storage of large amounts of data as required in unstructured grids are developed. Such grids are proposed to use for the efficient simulation of a wide class of electro physical devices. It is experimentally shown the need for a local modification of the rectangular grid in calculations in domains with curvilinear boundary. The two-step algorithms for local modifications of considered quasistructured grids are developed. On the first step modification of the near boundary nodes is carried out by the its shift along the normal to boundary and on the second step the transformation of the grid elements that do not meet the quality criteria in a quality grid elements is carried out. Special algorithms for such transformations, which do not violate the structuring subgrids in subdomains are developed. Recommendations for the construction of grids on the interface of subdomains that contain the uncoordinated grids have been done. Algorithms local modification of grids on the interface between the subdomains, one of which contains a segment of the computational domain boundaries, have been developed. The series of numerical experiments on solving a model problem are carried out. The results of numerical experiments showed the validity of the proposed approaches.

A BDDC algorithm with adaptive primal constraints for staggered discontinuous Galerkin approximation of elliptic problems with highly oscillating coefficients

A BDDC (Balancing Domain Decomposition by Constraints) algorithm for a staggered discontinuous Galerkin approximation is considered. After applying domain decomposition method, a global linear system on the subdomain interface unknowns is obtained and solved by the conjugate gradient method combined with a preconditioner. To construct a preconditioner that is robust to the coefficient variations, a generalized eigenvalue problem on each subdomain interface is solved and primal unknowns are selected from the eigenvectors using a predetermined tolerance. By the construction of the staggered discontinuous Galerkin methods, the degrees of freedom on subdomain interfaces are shared by only two subdomains, and hence the construction of primal unknowns are simplified. The resulting BDDC algorithm is shown to have the condition number bounded by the predetermined tolerance. A modified algorithm for parameter dependent problems is also introduced, where the primal unknowns are only computed in an offline stage. Numerical results are included to show the performance of the proposed method and to verify the theoretical estimate.

Power System Dynamic Simulations Using a Parallel Two-Level Schur-Complement Decomposition

As the need for faster power system dynamic simulations increases, it is essential to develop new algorithms that exploit parallel computing to accelerate those simulations. This paper proposes a parallel algorithm based on a two-level, Schur-complement-based, domain decomposition method. The two-level partitioning provides high parallelization potential (coarse- and fine-grained). In addition, due to the Schur-complement approach used to update the sub-domain interface variables, the algorithm exhibits high global convergence rate. Finally, it provides significant numerical and computational acceleration. The algorithm is implemented using the shared-memory parallel programming model, targeting inexpensive multi-core machines. Its performance is reported on a real system as well as on a large test system combining transmission and distribution networks.

An efficient parallel method for photo-realistic fluid animation

ABSTRACTFluid animation often appears in applications such as games, films and cartoons. How to animate photo-realistic fluid motion efficiently is an important issue. We present an efficient parallel method for photo-realistic fluid animation in this paper. Our method is designed to generate fluid animation results with high efficiency on a cluster system. To do this, we categorize the computers in our cluster system into two classes, the server and the client. The server controls the process of the fluid animation while the clients are responsible for numerical computation. Given 3D virtual environment and fluid initial condition, we make pre-processing on the server so as to decompose the fluid animation task into several subtasks. Thus, the computation domain is divided into blocks and each client executes numerical computation for one block. The blocks of two adjacent clients are overlapped to keep the continuity of the solution across subdomain interface. We demonstrate the efficiency of our method ...

SH3-like motif-containing C-terminal domain of staphylococcal teichoic acid transporter suggests possible function.

The negatively charged bacterial polysaccharides-wall teichoic acids (WTAs) are synthesized intracellularly and exported by a two-component transporter, TagGH, comprising a transmembrane subunit TagG and an ATPase subunit TagH. We determined the crystal structure of the C-terminal domain of TagH (TagH-C) to investigate its function. The structure shows an N-terminal SH3-like subdomain wrapped by a C-terminal subdomain with an anti-parallel β-sheet and an outer shell of α-helices. A stretch of positively charged surface across the subdomain interface is flanked by two negatively charged regions, suggesting a potential binding site for negatively charged polymers, such as WTAs or acidic peptide chains. Proteins 2016; 84:1328-1332. © 2016 Wiley Periodicals, Inc.

Composed Fluid–Structure Interaction Interface for Horizontal Axis Wind Turbine Rotor

In this paper, we propose a technique for high-fidelity fluid–structure interaction (FSI) spatial interface reconstruction of a horizontal axis wind turbine (HAWT) rotor model composed of an elastic blade mounted on a rigid hub. The technique is aimed at enabling re-usage of existing blade finite element method (FEM) models, now with high-fidelity fluid subdomain methods relying on boundary-fitted mesh. The technique is based on the partition of unity (PU) method and it enables fluid subdomain FSI interface mesh of different components to be smoothly connected. In this paper, we use it to connect a beam FEM model to a rigid body, but the proposed technique is by no means restricted to any specific choice of numerical models for the structure components or methods of their surface recoveries. To stress-test robustness of the connection technique, we recover elastic blade surface from collinear mesh and remark on repercussions of such a choice. For the HAWT blade recovery method itself, we use generalized Hermite radial basis function interpolation (GHRBFI) which utilizes the interpolation of small rotations in addition to displacement data. Finally, for the composed structure we discuss consistent and conservative approaches to FSI spatial interface formulations.

Metal Ion-Mediated Nucleobase Recognition by the ZTP Riboswitch

The ZTP riboswitch is a widespread family of regulatory RNAs that upregulate de novo purine synthesis in response to increased intracellular levels of ZTP or ZMP. As an important intermediate in purine biosynthesis, ZMP also serves as a proxy for the concentration of N10-formyl-tetrahydrofolate, a key component of one-carbon metabolism. Here, we report the structure of the ZTP riboswitch bound to ZMP at a resolution of 1.80 Å. The RNA contains two subdomains brought together through a long-range pseudoknot further stabilized through helix-helix packing. ZMP is bound at the subdomain interface of the RNA through a set of interactions with the base, ribose sugar, and phosphate moieties of the ligand. Unique to nucleobase recognition by RNAs, the Z base is inner-sphere coordinated to a magnesium cation bound by two backbone phosphates. This interaction, along with steric hindrance by the backbone, imparts specificity over chemically similar compounds such as ATP/AMP.

Structural analysis of a feline norovirus protruding domain

Norovirus infects different animals, including humans, mice, dogs, and cats. Here, we show an X-ray crystal structure of a feline GIV.2 norovirus capsid-protruding (P) domain to 2.35Å resolution. The feline GIV.2 P domain was reminiscent of human norovirus P domains, except for a novel P2 subdomain α-helix and an extended P1 subdomain interface loop. These new structural features likely obstructed histo-blood group antigens, which are attachment factors for human norovirus, from binding at the equivalent sites on the feline GIV.2 P domain. Additionally, an ELISA showed that the feline GIV.2 was antigenically distinct from a human GII.10 norovirus.

A monolithic multi-time-step computational framework for first-order transient systems with disparate scales

Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirable feature to have in a numerical formulation for multiscale transient problems is to be able to employ different time-steps (multi-time-step coupling), and different time integrators and different numerical formulations (mixed methods) in different regions of the computational domain. To this end, we present two new monolithic multi-time-step mixed coupling methods for first-order transient systems. We shall employ unsteady advection–diffusion–reaction equation with linear decay as the model problem, which offers several unique challenges in terms of non-self-adjoint spatial operator and rich features in the solutions. We shall employ the dual Schur domain decomposition technique to split the computational domain into an arbitrary number of subdomains. It will be shown that the governing equations of the decomposed problem, after spatial discretization, will be differential/algebraic equations. This is a crucial observation to obtain stable numerical results. Two different methods of enforcing compatibility along the subdomain interface will be used in the time discrete setting. A systematic theoretical analysis (which includes numerical stability, influence of perturbations, bounds on drift along the subdomain interface) will be performed. The first coupling method ensures that there is no drift along the subdomain interface, but does not facilitate explicit/implicit coupling. The second coupling method allows explicit/implicit coupling with controlled (but non-zero) drift in the solution along the subdomain interface. Several canonical problems will be solved to numerically verify the theoretical predictions, and to illustrate the overall performance of the proposed coupling methods. Finally, we shall illustrate the robustness of the proposed coupling methods using a multi-time-step transient simulation of a fast bimolecular advective–diffusive–reactive system.

Least squares approach for the time-dependent nonlinear Stokes–Darcy flow

A time-dependent nonlinear model of Stokes–Darcy flows is considered for numerical approximations by an optimization based domain decomposition method. The coupled system is formulated as a constrained optimal control problem, where a Neumann type control is introduced to enforce boundary conditions on the interface of subdomains. A computational algorithm is discussed for the least squares functional which measures the jump of flow balance across the interface. Numerical results are presented to validate convergence and accuracy of the method.

Analysis of reinforced and thin-walled structures by multi-line refined 1D/beam models

This paper focuses the attention on the use of appropriate combinations of refined one-dimensional (1D) beam theories to analyze thin-walled, reinforced structures. The cross-section of a slender body is seen as the sum of different sub-domains. Each sub-domain is subsequently used as the cross-section of a beam discretization. Displacement variables are then expanded around the beam axis of each sub-domain by using refined 1D models which are based on the Carrera Unified Formulation. The order of the beam elements can vary in different sub-domains. This subdivision has been called “multi-line” as opposed to the “one-line” approach of classical beam theories. 1D compatibility conditions of the displacements at selected points of the sub-domain interface boundaries are imposed by using Lagrange multipliers. Various problems have been analyzed to highlight the advantages and disadvantages of the present multi-line approach. It is concluded that the multi-line approach appears very effective in the case of thin-walled sections made by locally connected walls as well as in the case of reinforced structures.

A Subdomain Interaction at the Base of the Lever Allosterically Tunes the Mechanochemical Mechanism of Myosin 5a

The motor domain of myosin is the core element performing mechanochemical energy transduction. This domain contains the actin and ATP binding sites and the base of the force-transducing lever. Coordinated subdomain movements within the motor are essential in linking the ATPase chemical cycle to translocation along actin filaments. A dynamic subdomain interface located at the base of the lever was previously shown to exert an allosteric influence on ATP hydrolysis in the non-processive myosin 2 motor. By solution kinetic, spectroscopic and ensemble and single-molecule motility experiments, we determined the role of a class-specific adaptation of this interface in the mechanochemical mechanism of myosin 5a, a processive intracellular transporter. We found that the introduction of a myosin 2-specific repulsive interaction into myosin 5a via the I67K mutation perturbs the strong-binding interaction of myosin 5a with actin, influences the mechanism of ATP binding and facilitates ATP hydrolysis. At the same time, the mutation abolishes the actin-induced activation of ADP release and, in turn, slows down processive motility, especially when myosin experiences mechanical drag exerted by the action of multiple motor molecules bound to the same actin filament. The results highlight that subtle structural adaptations of the common structural scaffold of the myosin motor enable specific allosteric tuning of motor activity shaped by widely differing physiological demands.

A Nonoverlapping Domain Decomposition Method for Incompressible Stokes Equations with Continuous Pressures

A nonoverlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressure component is enforced in the primal form, i.e., neighboring subdomains share the same pressure degrees of freedom on the subdomain interface and no Lagrange multipliers are needed. After eliminating all velocity variables and the independent subdomain interior parts of the pressures, a symmetric positive semidefinite linear system for the subdomain boundary pressures and the Lagrange multipliers is formed and solved by a preconditioned conjugate gradient method. A lumped preconditioner is studied and the condition number bound of the preconditioned operator is proved to be independent of the number of subdomains fo...