Sparse Mode Research Articles

A 3-D finite-element algorithm for DC resistivity modelling using the shifted incomplete Cholesky conjugate gradient method

SUMMARY An accurate and efficient 3-D finite-element (FE) forward algorithm for DC resistivity modelling is developed. First, the total potential is decomposed into the primary potential caused by the source current and the secondary potential caused by changes in the electrical conductivity. Then, the boundary value problem for the secondary field and its equivalent variational problem are presented, where the finite-element method is used. This removes the singularity caused by the primary potential, resulting in an accurate 3-D resistivity model. Secondly, I introduce the row-indexed sparse storage mode to store the coefficient matrix and the shifted incomplete Cholesky conjugate gradient (SICCG) iterative method to solve the large linear system derived from the 3-D FE calculation. The SICCG method converges very quickly and requires much less computer storage, while the traditional ICCG or modified ICCG (MICCG) method usually fails for an irregular grid. The SICCG method is more efficient than the direct method, i.e. the elimination solver with the banded Cholesky factorization. Also, it has an advantage over the symmetric successive overrelaxation preconditioning conjugate gradient method. Numerical examples of a three-layered model with high conductivity contrast and a vertical contact show that the results from the secondary potential FE method agree well with analytic solutions. With the same grid nodes, much higher accuracy from the solution of the secondary potential than those solving the total potential can be achieved. Also a 3-D cubic body is simulated, and the dipole–dipole apparent resistivities agree well with the results from other methods. By defining the analytical solution of a vertical contact as the primary potential, a more complicated model with several 3-D inhomogeneities near the vertical contact is simulated. The presented method also obtains good results for this model.

Three‐Dimensional Finite‐Element Forward Modeling of Resistivity using the Conjugate Gradient Algorithm

AbstractThe symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient algorithm is used to solve large linear systems derived from 3‐D finite‐element resistivity forward modeling. Combined with the row‐indexed sparse storage mode to store coefficient matrix, the algorithm converges much quickly and requires much less storage of computer. It is very convenient to be applied to the solution of the secondary potential, achieving much higher accuracy while the calculation is keeping fast.

Rendezvous point relocation in protocol independent multicast - sparse mode

Protocol independent multicast - sparse mode is the most widely used multicast routing architecture. It builds a shared distribution tree centered at a rendezvous point and then builds source-specific trees for those sources whose data rate warrants it. Current implementations of the protocol decide on the rendezvous point administratively, which leads to congestion and delays. An attractive solution would be dynamic relocation of the rendezvous point depending on the members of the multicast group. We present a rendezvous point calculation and relocation mechanism for protocol independent multicast -sparse mode. Simulation of the proposed mechanisms is used to demonstrate the effectiveness of the proposals.

Distributed core multicast (DCM)

We present a multicast routing protocol called Distributed Core Multicast (DCM). It is intended for use within a large single Internet domain network with a very large number of multicast groups with a small number of receivers. Such a case occurs, for example, when multicast addresses are allocated to mobile hosts, as a mechanism to manage Internet host mobility or in large distributed simulations. For such cases, existing dense or sparse mode multicast routing algorithms do not scale well with the number of multicast groups. DCM is based on an extension of the centre-based tree approach. It uses several core routers, called Distributed Core Routers (DCRs) and a special control protocol among them. DCM aims: (1) avoiding multicast group state information in backbone routers, (2) avoiding triangular routing across expensive backbone links, (3) scaling well with the number of multicast groups. We evaluate the performance of DCM and compare it to an existing sparse mode routing protocol when there is a large number of small multicast groups. We also analyse the behaviour of DCM when the number of receivers per group is not a small number.

Antiphase Q-switch dynamics in a multimode solid-state laser with saturable absorber

Antiphase Q-switch dynamics in a multimode solid-state laser with saturable absorber is investigated both experimentally and theoretically. The system under study is a large cavity, longitudinally pumped Nd:YAG laser with Cr 4+:YAG as saturable absorber. Asymmetric two-mode operation was found for a wide range of control parameters. To describe the sparse mode distribution, a multimode rate equation system was developed that accounts for spatial grating in the active medium and non-linear absorption. The model is shown to predict pulse sequences experimentally observed as the pump parameter is changed. For high pump ratios a quasi-pure periodic antiphase state is recovered which consists of two modes pulsing with the same period T and shifted by T/2. It is then conjectured that an apparent symmetry of the system can be established for certain values of the control parameters.

A multichannel readout electronics for nuclear application (RENA) chip developed for position sensitive solid state detectors

A multichannel mixed signal Application Specific Integrated Circuit (ASIC) chip for front end readout electronics of position sensitive solid state detectors has been developed. It is called Readout Electronics for Nuclear Applications (RENA). This chip can be used for large number of channels and high-energy resolution astrophysics and nuclear physics detectors. It can also be applied for medical and industrial imaging of X-rays and gamma rays. The RENA chip is a monolithic integrated circuit and has 32 channels with low-noise high input impedance charge sensitive amplifiers. It works in pulse counting mode with good energy resolution. It also has a self-triggering output which is essential for nuclear applications when the incident radiation arrives at random. Different, externally selectable, operational modes that includes a sparse readout mode is available to increase data throughput. It also has externally selectable shaping (peaking) times. A full-scale prototype RENA chip version III is being manufactured. The results of tests done on the third prototype chip connected to a CdZnTe pad detector array will be presented.

Approximate Inverse Preconditioners via Sparse-Sparse Iterations

The standard incomplete LU (ILU) preconditioners often fail for general sparse indefinite matrices because they give rise to unstable factors L and U. In such cases, it may be attractive to approximate the inverse of the matrix directly. This paper focuses on approximate inverse preconditioners based on minimizing ||I-AM||F, where AM is the preconditioned matrix. An iterative descent-type method is used to approximate each column of the inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., with sparse-matrix by sparse-vector operations. Numerical dropping is applied to maintain sparsity; compared to previous methods, this is a natural way to determine the sparsity pattern of the approximate inverse. This paper describes Newton, global, and column-oriented algorithms, and discusses options for initial guesses, self-preconditioning, and dropping strategies. Some limited theoretical results on the properties and convergence of approximate inverses are derived. Numerical tests on problems from the Harwell--Boeing collection and the FIDAP fluid dynamics analysis package show the strengths and limitations of approximate inverses. Finally, some ideas and experiments with practical variations and applications are presented.

Policy tree multicast routing

Bandwidth-sensitive multicast delivery controlled by routing criteria pertinent to the actual traffic flow is very costly in terms of router state and control overhead and it scales poorly towards larger, wide-area networks. PIM-SM (Protocol-independent Multicast - Sparse Mode) has been introduced as a simple, flexible and scalable concept for Internet-wide multicasting. Yet, PIM's efficiency potential (like that of alternative wide-area multicast concepts) can only be fully exploited if it is based on Reverse Path Forwarding (RPF), a low-cost mechanism, which however does not select prescribed delivery paths if link parameters or routing policies are asymmetric. This paper presents an extension to protocols like PIM-SM, called Policy Tree Multicast Routing (PTMR). This concept leads to multicast delivery trees which, even under asymmetric conditions, readily comply with imposed macroscopic policies and moreover enable support of shortest path and QoS criteria. PTMR gives no consideration to how the policy-sensitive paths have been established; they may be imposed by the network itself but also by providers, recipients and even sources. PTMR amends the PIM-SM mechanism with a macroscopic control layer which marks (pegs) domain border routers on policy-sensitive forward paths. In a given domain, a pegged ingress border router is then joined by local group members as well as by its child pegs. This results in optimally fusing transit paths into local distribution trees. PTMR performance and policy control potential are restricted primarily: by the congestion of control messages at the multicast sources, introduced by source-originating tree construction; by the possible extent of policy-sensitive path aggregation; and by the intra-domain (transit) delivery conditions. PTMR is a single-layer protocol, appending PIM-SM with a policy dedicated delivery mode. Ist primary design target is to forward multicast traffic in accordance with any underlying multicast-relevant routing, including comprehensive policy routing. In comparison, Border Gateway Multicast Protocol (BGMP) is a proposal for an intra-domain MR protocol based on BGP-type routing, which focuses on fusing heterogenous multicast routing domains and which allows ASs to control multicast transit traffic.

Performance and resource cost comparisons for the CBT and PIM multicast routing protocols

Researchers have proposed the core-based trees (CBTs) and protocol independent multicasting (PIM) protocols to route multicast data an internetworks. We compare the simulated performance of CBT and PIM using the OPNET network simulation tool. Performance metrics include end-to-end delay, network resource usage, join time, the size of the tables containing multicast routing information, and the impact of the timers introduced by the protocols. We also offer suggestions to improve PIM sparse mode while retaining the ability to offer both shared tree and source-based tree routing.

A Front End Readout Electronics ASIC Chip for Position Sensitive Solid State Detectors

AbstractA mixed signal Application Specific Integrated Circuit (ASIC) chip for front end readout electronics of position sensitive solid state detectors has been manufactured. It is called RENA (Readout Electronics for Nuclear Applications). This chip can be used for both medical and industrial imaging of x-rays and gamma rays. The RENA chip is a monolithic integrated circuit and has 32 channels with low noise high input impedance charge sensitive amplifiers. It works in pulse counting mode with good energy resolution. It also has a self triggering output which is essential for nuclear applications when the incident radiation arrives at random. Different, externally selectable, operational modes that includes a sparse readout mode is available to increase data throughput. It also has externally selectable shaping (peaking) times.