PLTMGC swMATH ID: 1063 Software Authors: Bank, Randolph E.; Chan, Tony F. Description: PLTMGC is a program package for solving nonlinear elliptic systems that have explicit dependence on a scalar parameter. In addition to being able to compute solutions for fixed parameter values, it can be used to solve the linear eigenvalue problem, trace solution branches, locate singular points (simple turning points and bifurcation points) and switch branch at simple bifurcation points. A multi-grid continuation approach is employed in which a continuation procedure is used to follow the solution curve on the coarset grid and a multi-grid algorithm is used to refine the solution at selected points using an adaptive mesh refinement strategy. Some numerical examples illustrating the performance of the package are given. Homepage: http://epubs.siam.org/sisc/resource/1/sjoce3/v7/i2/p540_s1?isAuthorized=no Keywords: continuation methods; PLTMGC; program package; linear eigenvalue problem; trace solution branches; singular points; turning points; bifurcation points; multi-grid algorithm; adaptive mesh refinement; numerical examples Related Software: LOCA; PLTMG; GPFEM; BVPh; ABC4EFT; Z; Cross; CLT; symrcm; OEIS; Petruchio; AIM@SHAPE; PcGets; CGS; PITCON; TRANSPORT; CHEMKIN; ALCON Cited in: 19 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year PLTMGC: A multi-grid continuation program for parameterized nonlinear elliptic systems. Zbl 0589.65074Bank, Randolph E.; Chan, Tony F. 1986 all top 5 Cited by 34 Authors 3 Zhou, Jianxin 2 Chan, Tony Fan-Cheong 2 Chien, Cheng-Sheng 2 Li, Zhaoxiang 1 Allgower, Eugene L. 1 Bank, Randolph E. 1 Bell, John B. 1 Berger, Alan E. 1 Boyd, John Philip 1 Chang, Shing-Lin 1 Gao, Yali 1 García-Archilla, Bosco 1 Georg, Kurt 1 Giovangigli, Vincent 1 Gloria, Antoine 1 Jeng, B.-W. 1 Juncu, Gheorghe 1 Kapania, Rakesh K. 1 Liao, Shijun 1 Mei, Liquan 1 Moret, Igor 1 Mosekilde, Erik 1 Popa, Constantin 1 Simó, Carles 1 Smooke, Mitchell D. 1 Solomon, Jay M. 1 Syam, Muhammed I. 1 Szymczak, William G. 1 Tai, Xuecheng 1 Tseng, Paul 1 Wang, Zhi-Qiang 1 Xie, Ziqing 1 Yang, Zhaochen 1 Yi, Wenfan all top 5 Cited in 12 Serials 4 Journal of Computational and Applied Mathematics 2 Mathematics of Computation 2 Applied Numerical Mathematics 2 Journal of Scientific Computing 1 Computers & Mathematics with Applications 1 BIT 1 Computing 1 Numerische Mathematik 1 SIAM Journal on Scientific and Statistical Computing 1 Computational Mechanics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Communications in Nonlinear Science and Numerical Simulation all top 5 Cited in 10 Fields 19 Numerical analysis (65-XX) 12 Partial differential equations (35-XX) 2 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year