Implementation of Basic Operations for Sparse Matrices when Solving a Generalized Eigenvalue Problem in the ACELAN-COMPOS Complex

Introduction. The widespread use of piezoelectric materials in various industries stimulates the study their physical characteristics and determines urgency such research. In this case, modal analysis makes it possible to determine operating frequency coefficient electromechanical coupling elements devices. These indicators are serious theoretical applied interest. was aimed at development numerical methods for solving problem determining resonance frequencies a system elastic bodies. To achieve goal, we needed new approaches discretization based on finite element method execution software implementation selected C# .net platform. Current solutions were created context ACELAN-COMPOS class library. known generalized eigenvalue matrix inversion not applicable large-dimensional matrices. overcome limitation, presented scientific work implemented logic constructing mass matrices interfaces exchanging data problems with pre- postprocessing modules. Materials Methods. A platform used implement programming language. Validation research results carried out through comparing values found obtained well-known SAE packages (computer-aided engineering). routines evaluated terms performance applicability large-scale tasks. Numerical experiments validate algorithms small-dimensional that solved by MATLAB. Next, approach tested tasks large number unknowns taking into account parallelization individual operations. avoid finding inverse matrix, modified Lanczos programmatically implemented. We examined formats storing RAM: triplets, CSR, СSC, Skyline. solve linear algebraic equations (SLAE), an iterative symmetric LQ adapted these storage used. Results. New calculation modules integrated library complex developed. Calculations sparse RAM implementing operations structure stiffness constructed same task, but different renumbering nodes grid, graphically visualized. relation theory electroelasticity, time required perform basic summarized form table. It has been established grid gives significant increase even without changing internal memory. Taking objectives study, advantages weaknesses named. Thus, CSR optimal when multiplying vector, SKS inverting matrix. order 10 3 , won speed. evaluated. contribution all total solution measured. operation SLAE takes up 95% algorithm. When method, greatest computational costs multiply vector. algorithm, shared memory resorted to. using eight threads, gain increased 40–50%. Discussion Conclusion. as part package. Their model quasi-regular grids estimated. features structures electroelastic body, preferred processing determined.