This technology is a numerical analysis method that significantly reduces computational complexity by linearizing nonlinear terms using Taylor approximation and performing LU decomposition on matrices, enabling efficient solving of high-dimensional partial differential equation-based models like P2D for analyzing physical reactions in lithium-ion batteries.
While conventional P2D models can precisely represent internal battery states, they suffer from high computational costs. In particular, as electrode dimensions increase, the computational load grows exponentially—often exceeding the fourth power of the grid count—making real-time internal state prediction in BMS challenging.
This technology converts model equations into time-step-based difference equations, linearizes nonlinear term vectors via Taylor approximation to avoid iterative calculations, and uses LU decomposition to isolate independent operations. By applying approximate factorization to high-dimensional matrices, it reduces computational complexity from O(n^9) to O(n^3). It can be applied to onboard electrochemical models for vehicle BMS, digital twins for cell design, and fast-charging profile optimization software, allowing real-time tracking of lithium concentration and potential distribution even on low-spec embedded processors.
This invention was developed with support from the Ministry of Science and ICT's Applied Analysis and Computing Center.
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