The Experts below are selected from a list of 6498 Experts worldwide ranked by ideXlab platform
Yongping Wang - One of the best experts on this subject based on the ideXlab platform.
-
three dimensional variational nodal method parallelization for pin resolved neutron transport calculations
Progress in Nuclear Energy, 2019Co-Authors: Yongping Wang, Tengfei Zhang, E E Lewis, W S Yang, M A SmithAbstract:Abstract Hybrid parallelization of the three-dimensional variational nodal method (VNM) for pin-resolved neutron transport calculations is presented. Sets of node-energy response and associated matrices are assigned evenly to the available set of MPI processors and OpenMP is further employed to parallelize integrations over angle in the response Matrix formation. Parallelization of the solution algorithm is accomplished using non-overlapping domain decomposition with one MPI processor assigned to each subdomain. Additionally, the red and black subdomain iterations of the within-group equations are parallelized by OpenMP. Only the pre-calculated Matrix sets needed in a subdomain are stored in the corresponding processor. This parallel solution strategy preserves the block Gauss-Seidel red-black iterations employed in serial calculation, with data transfer between processors only after each red and black iteration. Partitioned Matrix acceleration is implemented in a similar manner. These parallel algorithms are implemented in the code PANX allowing both higher-order space-angle approximations to be employed and larger spatial domains to be treated than was the case with the serial form of the code. The KAIST problem is used to both evaluate the parallel performance and demonstrate the increased accuracy of the higher-order angular approximations. With 27 MPI processors and 4 OpenMP threads, speedups of nearly 39 are obtained. To demonstrate the applicability of parallel algorithms to larger spatial domains, a pin-resolved, three-dimensional seven-group model of the NuScale modular reactor core with sufficiently high order space-angle discretization is employed using 49 MPI processors and 4 OpenMP threads, and completed in 4 h with P3 approximation.
-
generalized Partitioned Matrix acceleration for variational nodal diffusion method
Nuclear Science and Engineering, 2019Co-Authors: Yongping Wang, Tengfei Zhang, E E Lewis, M A Smith, Won Sik YangAbstract:AbstractThe Generalized Partitioned Matrix (GPM) acceleration method for the Variational Nodal Method (VNM) with diffusion approximation is presented. In the GPM method, the vectors of expansion coefficients of the scalar flux, source, and partial currents are divided into low-order and high-order terms. For each outer iteration, the low-order terms of the flux, fission source, and partial currents are first solved with fixed higher-order terms from the preceding outer iteration, and then a full Matrix sweep through the energy groups is performed to update the full set of expansion coefficients. The GPM method increases the CPU time per outer iteration but reduces the overall computational time significantly by reducing the number of outer iterations required for convergence. The GPM acceleration method has been implemented in the NODAL code, and its performance was compared with that of the traditional Partitioned Matrix (PM) acceleration scheme for four problems: two- and three-dimensional C5G7 problems...
-
generalized Partitioned Matrix acceleration for variational nodal diffusion method
Nuclear Science and Engineering, 2019Co-Authors: Yongping Wang, Tengfei Zhang, E E Lewis, M A Smith, Won Sik YangAbstract:The Generalized Partitioned Matrix (GPM) acceleration method for the Variational Nodal Method (VNM) with diffusion approximation is presented. In the GPM method, the vectors of expansion coefficien...
-
Partitioned-Matrix acceleration to the Fission-Source iteration of the Variational Nodal Method
Progress in Nuclear Energy, 2015Co-Authors: Yongping Wang, Boning Liang, Wei ShenAbstract:Abstract The Variational Nodal Method (VNM) expands the nodal volumetric flux and surface partial current into the sums of orthogonal basis functions without using the transverse integration technique. The exclusion of the transverse integration provides a number of advantages for employing the VNM in Pressurized Water Reactor (PWR) core simulation. The orthogonality of those basis functions guarantees the conservation of neutron balance regardless of the expansion orders, providing an opportunity to accelerate the computationally expensive full-order iteration by using cheap low-order sweeping with high-order moments fixed. This was named as the Partitioned-Matrix (PM) technique in the legacy VNM code VARIANT, and was applied to the within-group (WG) iteration. It is very effective for neutron-transport calculation, but less effective for neutron-diffusion mainly due to the reduced number of high-order partial current moments. In this paper, we extend the PM technique to the Fission-Source (FS) iteration to accelerate the flux convergence by using low-order flux moments also. From the macroscopic acceleration point of view, it converges the fission- and scattering-source distributions by using computationally cheap low-order iteration faster than the original full-order sweeping. Based on our new VNM code VIOLET, considering the fact that the discontinuity factor used for preserving neutron leakage rates during spatial homogenization slows down the nodal iteration convergence, numerical tests were carried out for two typical PWR problems respectively without and with discontinuity factors. By analyzing both the computational effort in terms of FLOP (FLoating-point OPeration) and computing time, the following conclusions have been demonstrated. The legacy PM technique for WG iteration can provide an acceleration ratio of about 2 for the PWR core neutron-diffusion calculation with or without using discontinuity factors, while the one for FS iteration itself can accelerate by a factor of about 3 which is higher. By accelerating both the WG and FS iteration simultaneously, the acceleration ratio is about 4 for both the two PWR problems. In addition, by extending the PM technique from the WG iteration to the FS iteration, the neutron-diffusion calculation of the VNM can be accelerated very effectively with almost no extra storage or implementation cost to the existing computer code.
Stephen A Morse - One of the best experts on this subject based on the ideXlab platform.
-
asynchronous distributed algorithms for solving linear algebraic equations
IEEE Transactions on Automatic Control, 2018Co-Authors: Stephen A MorseAbstract:Two asynchronous distributed algorithms are presented for solving a linear equation of the form $Ax=b$ with at least one solution. The equation is simultaneously and asynchronously solved by $m$ agents assuming that each agent knows only a subset of the rows of the Partitioned Matrix $[A\ \ b]$ , the estimates of the equation's solution generated by its neighbors, and nothing more. Neighbor relationships are characterized by a time-dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relationships. Each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by its neighbors which are transmitted with delays. The event time sequences of different agents are not assumed to be synchronized. It is shown that for any Matrix-vector pair $(A, b)$ for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents’ event times, the algorithms cause all agents’ estimates to converge exponentially fast to the same solution to $Ax=b$ . The first algorithm requires a specific initialization step at each agent, and the second algorithm works for arbitrary initializations. Explicit expressions for convergence rates are provided, and a relation between local initializations and limiting consensus solutions is established, which is used to solve the least 2-norm solution.
-
a distributed algorithm for solving a linear algebraic equation
IEEE Transactions on Automatic Control, 2015Co-Authors: Shaoshuai Mou, Ji Liu, Stephen A MorseAbstract:A distributed algorithm is described for solving a linear algebraic equation of the form $Ax = b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of the rows of the Partitioned Matrix $[\Matrix{A & b}]$ , the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph $\BBN(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any Matrix $A$ for which the equation has a solution and any sequence of “repeatedly jointly strongly connected graphs” $\BBN(t)$ , $t = 1, 2, \ldots$ , the algorithm causes all agents' estimates to converge exponentially fast to the same solution to $Ax = b$ . It is also shown that, under mild assumptions, the neighbor graph sequence must actually be repeatedly jointly strongly connected if exponential convergence is to be assured. A worst case convergence rate bound is derived for the case when $Ax = b$ has a unique solution. It is demonstrated that with minor modification, the algorithm can track the solution to $Ax = b$ , even if $A$ and $b$ are changing with time, provided the rates of change of $A$ and $b$ are sufficiently small. It is also shown that in the absence of communication delays, exponential convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors. A modification of the algorithm is outlined which enables it to obtain a least squares solution to $Ax = b$ in a distributed manner, even if $Ax = b$ does not have a solution.
-
a distributed algorithm for solving a linear algebraic equation
arXiv: Systems and Control, 2015Co-Authors: Shaoshuai Mou, Ji Liu, Stephen A MorseAbstract:A distributed algorithm is described for solving a linear algebraic equation of the form $Ax=b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of the rows of the Partitioned Matrix $(A,b)$, the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph $\mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any Matrix $A$ for which the equation has a solution and any sequence of "repeatedly jointly strongly connected graphs" $\mathbb{N}(t)$, $t=1,2,\ldots$, the algorithm causes all agents' estimates to converge exponentially fast to the same solution to $Ax=b$. It is also shown that the neighbor graph sequence must actually be repeatedly jointly strongly connected if exponential convergence is to be assured. A worst case convergence rate bound is derived for the case when $Ax=b$ has a unique solution. It is demonstrated that with minor modification, the algorithm can track the solution to $Ax = b$, even if $A$ and $b$ are changing with time, provided the rates of change of $A$ and $b$ are sufficiently small. It is also shown that in the absence of communication delays, exponential convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors. A modification of the algorithm is outlined which enables it to obtain a least squares solution to $Ax=b$ in a distributed manner, even if $Ax=b$ does not have a solution.
-
an asynchronous distributed algorithm for solving a linear algebraic equation
Conference on Decision and Control, 2013Co-Authors: Ji Liu, Shaoshuai Mou, Stephen A MorseAbstract:A distributed algorithm is described for solving a linear algebraic equation of the form Ax = b where A is a Matrix for which the equation has at least one solution. The equation is simultaneously and asynchronously solved by m agents assuming each agent knows only a subset of the rows of the Partitioned Matrix [A b], the estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by each of its neighbors which are transmitted with delays. Each agent has its own event time sequence and the event time sequences of different agents are not assumed to be synchronized. Neighbor relations are characterized by a time-dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any Matrix A for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents' event times, the algorithm causes all agents' estimates to converge exponentially fast to the same solution to Ax = b.
Shaoshuai Mou - One of the best experts on this subject based on the ideXlab platform.
-
a distributed algorithm for solving a linear algebraic equation
IEEE Transactions on Automatic Control, 2015Co-Authors: Shaoshuai Mou, Ji Liu, Stephen A MorseAbstract:A distributed algorithm is described for solving a linear algebraic equation of the form $Ax = b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of the rows of the Partitioned Matrix $[\Matrix{A & b}]$ , the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph $\BBN(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any Matrix $A$ for which the equation has a solution and any sequence of “repeatedly jointly strongly connected graphs” $\BBN(t)$ , $t = 1, 2, \ldots$ , the algorithm causes all agents' estimates to converge exponentially fast to the same solution to $Ax = b$ . It is also shown that, under mild assumptions, the neighbor graph sequence must actually be repeatedly jointly strongly connected if exponential convergence is to be assured. A worst case convergence rate bound is derived for the case when $Ax = b$ has a unique solution. It is demonstrated that with minor modification, the algorithm can track the solution to $Ax = b$ , even if $A$ and $b$ are changing with time, provided the rates of change of $A$ and $b$ are sufficiently small. It is also shown that in the absence of communication delays, exponential convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors. A modification of the algorithm is outlined which enables it to obtain a least squares solution to $Ax = b$ in a distributed manner, even if $Ax = b$ does not have a solution.
-
a distributed algorithm for solving a linear algebraic equation
arXiv: Systems and Control, 2015Co-Authors: Shaoshuai Mou, Ji Liu, Stephen A MorseAbstract:A distributed algorithm is described for solving a linear algebraic equation of the form $Ax=b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of the rows of the Partitioned Matrix $(A,b)$, the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph $\mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any Matrix $A$ for which the equation has a solution and any sequence of "repeatedly jointly strongly connected graphs" $\mathbb{N}(t)$, $t=1,2,\ldots$, the algorithm causes all agents' estimates to converge exponentially fast to the same solution to $Ax=b$. It is also shown that the neighbor graph sequence must actually be repeatedly jointly strongly connected if exponential convergence is to be assured. A worst case convergence rate bound is derived for the case when $Ax=b$ has a unique solution. It is demonstrated that with minor modification, the algorithm can track the solution to $Ax = b$, even if $A$ and $b$ are changing with time, provided the rates of change of $A$ and $b$ are sufficiently small. It is also shown that in the absence of communication delays, exponential convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors. A modification of the algorithm is outlined which enables it to obtain a least squares solution to $Ax=b$ in a distributed manner, even if $Ax=b$ does not have a solution.
-
an asynchronous distributed algorithm for solving a linear algebraic equation
Conference on Decision and Control, 2013Co-Authors: Ji Liu, Shaoshuai Mou, Stephen A MorseAbstract:A distributed algorithm is described for solving a linear algebraic equation of the form Ax = b where A is a Matrix for which the equation has at least one solution. The equation is simultaneously and asynchronously solved by m agents assuming each agent knows only a subset of the rows of the Partitioned Matrix [A b], the estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by each of its neighbors which are transmitted with delays. Each agent has its own event time sequence and the event time sequences of different agents are not assumed to be synchronized. Neighbor relations are characterized by a time-dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any Matrix A for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents' event times, the algorithm causes all agents' estimates to converge exponentially fast to the same solution to Ax = b.
-
a distributed algorithm for solving a linear algebraic equation
Allerton Conference on Communication Control and Computing, 2013Co-Authors: Shaoshuai Mou, Ji Liu, A S MorseAbstract:A distributed algorithm is described for solving a linear algebraic equation of the form Ax = b where A is a Matrix for which the equation has at least one solution. The equation is simultaneously solved by m agents assuming each agent knows only a subset of the rows of the Partitioned Matrix [A b], the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate of a solution by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph N(t) whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any Matrix A for which the equation has a solution and any sequence of “repeatedly jointly strongly connected graphs” N(t), t = 1, 2, ..., the algorithm causes all agents' estimates to converge exponentially fast to the same solution to Ax = b. It is also shown that in the absence of transmission delays, convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors.
-
a fixed neighbor distributed algorithm for solving a linear algebraic equation
European Control Conference, 2013Co-Authors: Shaoshuai Mou, A S MorseAbstract:This paper presents a distributed algorithm for solving a linear algebraic equation of the form Ax = b where A is an n × n nonsingular Matrix and b is an n-vector. The equation is solved by a network of n agents assuming that each agent knows exactly one distinct row of the Partitioned Matrix [A b], the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate of A-1b by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a simple, undirected graph G whose vertices correspond to agents and whose edges depict neighbor relations. It is shown that for any nonsingular Matrix A and any connected graph G, the proposed algorithm causes all agents' estimates to converge exponentially fast to the desired solution A-1b.
M A Smith - One of the best experts on this subject based on the ideXlab platform.
-
three dimensional variational nodal method parallelization for pin resolved neutron transport calculations
Progress in Nuclear Energy, 2019Co-Authors: Yongping Wang, Tengfei Zhang, E E Lewis, W S Yang, M A SmithAbstract:Abstract Hybrid parallelization of the three-dimensional variational nodal method (VNM) for pin-resolved neutron transport calculations is presented. Sets of node-energy response and associated matrices are assigned evenly to the available set of MPI processors and OpenMP is further employed to parallelize integrations over angle in the response Matrix formation. Parallelization of the solution algorithm is accomplished using non-overlapping domain decomposition with one MPI processor assigned to each subdomain. Additionally, the red and black subdomain iterations of the within-group equations are parallelized by OpenMP. Only the pre-calculated Matrix sets needed in a subdomain are stored in the corresponding processor. This parallel solution strategy preserves the block Gauss-Seidel red-black iterations employed in serial calculation, with data transfer between processors only after each red and black iteration. Partitioned Matrix acceleration is implemented in a similar manner. These parallel algorithms are implemented in the code PANX allowing both higher-order space-angle approximations to be employed and larger spatial domains to be treated than was the case with the serial form of the code. The KAIST problem is used to both evaluate the parallel performance and demonstrate the increased accuracy of the higher-order angular approximations. With 27 MPI processors and 4 OpenMP threads, speedups of nearly 39 are obtained. To demonstrate the applicability of parallel algorithms to larger spatial domains, a pin-resolved, three-dimensional seven-group model of the NuScale modular reactor core with sufficiently high order space-angle discretization is employed using 49 MPI processors and 4 OpenMP threads, and completed in 4 h with P3 approximation.
-
generalized Partitioned Matrix acceleration for variational nodal diffusion method
Nuclear Science and Engineering, 2019Co-Authors: Yongping Wang, Tengfei Zhang, E E Lewis, M A Smith, Won Sik YangAbstract:AbstractThe Generalized Partitioned Matrix (GPM) acceleration method for the Variational Nodal Method (VNM) with diffusion approximation is presented. In the GPM method, the vectors of expansion coefficients of the scalar flux, source, and partial currents are divided into low-order and high-order terms. For each outer iteration, the low-order terms of the flux, fission source, and partial currents are first solved with fixed higher-order terms from the preceding outer iteration, and then a full Matrix sweep through the energy groups is performed to update the full set of expansion coefficients. The GPM method increases the CPU time per outer iteration but reduces the overall computational time significantly by reducing the number of outer iterations required for convergence. The GPM acceleration method has been implemented in the NODAL code, and its performance was compared with that of the traditional Partitioned Matrix (PM) acceleration scheme for four problems: two- and three-dimensional C5G7 problems...
-
generalized Partitioned Matrix acceleration for variational nodal diffusion method
Nuclear Science and Engineering, 2019Co-Authors: Yongping Wang, Tengfei Zhang, E E Lewis, M A Smith, Won Sik YangAbstract:The Generalized Partitioned Matrix (GPM) acceleration method for the Variational Nodal Method (VNM) with diffusion approximation is presented. In the GPM method, the vectors of expansion coefficien...
Yanyang Liang - One of the best experts on this subject based on the ideXlab platform.
-
an efficient algorithm for the incremental broad learning system by inverse cholesky factorization of a Partitioned Matrix
IEEE Access, 2021Co-Authors: Hufei Zhu, Zhulin Liu, C Philip L Chen, Yanyang LiangAbstract:In this paper, we propose an efficient algorithm to accelerate the existing Broad Learning System (BLS) algorithm for new added nodes. The existing BLS algorithm computes the output weights from the pseudoinverse with the ridge regression approximation, and updates the pseudoinverse iteratively. As a comparison, the proposed BLS algorithm computes the output weights from the inverse Cholesky factor of the Hermitian Matrix in the calculation of the pseudoinverse, and updates the inverse Cholesky factor efficiently. Since the Hermitian Matrix in the definition of the pseudoinverse is smaller than the pseudoinverse, the proposed BLS algorithm can reduce the computational complexity, and usually requires less than $\frac {2}{3}$ of complexities with respect to the existing BLS algorithm. Our experiments on the Modified National Institute of Standards and Technology (MNIST) dataset show that the speedups in accumulative training time and each additional training time of the proposed BLS over the existing BLS are 24.81%~ 37.99% and 36.45%~ 58.96%, respectively, and the speedup in total training time is 37.99%. In our experiments, the proposed BLS and the existing BLS both achieve the same testing accuracy when the tiny differences (≤ 0.05%) caused by the numerical errors are neglected, and the above-mentioned tiny differences and numerical errors become zeroes and ignorable, respectively, when the ridge parameter is not too small.