阅读说明：本技术 键基近场动力学的并行立方晶格积分法 (Parallel cubic lattice integration method of bond-based near-field dynamics ) 是由 曹卓 钱松荣 石敏 冉秀 王剑锋 王勇 于 2019-08-19 设计创作，主要内容包括：本发明公开了一种键基近场动力学的并行立方晶格积分法,主要针对循环计算进行并行化处理；对三个循环进行分析可知,在时间步循环中,前后时间步间具有依赖关系,即下一时间步需要使用前一时间步的计算结果,故不可并行,而在点单元间的循环和每个点单元的所有键的循环中,点单元间的计算和每个点单元的所有键的计算都是独立的,因此可进行并行化处理,并行化处理后的数值计算过程如图3所示,其中将单元点循环和键循环采用多进程的并行计算方式,可有效提高数值计算速度,且计算结果与不采用并行计算时的结果一致。选择适当的并行进程数量可在一定的硬件条件下有效提高计算效率,适用性较广。(The invention discloses a parallel cubic lattice integration method of bond-based near-field dynamics, which mainly carries out parallel processing aiming at loop calculation; as can be seen from the analysis of the three loops, in the time step loop, there is a dependency relationship between previous and next time steps, that is, the next time step needs to use the calculation result of the previous time step, and therefore, the loop between the point units and the loop of all keys of each point unit are not parallel to each other, and the calculation between the point units and the calculation of all keys of each point unit are independent from each other, so that the parallelization processing can be performed, and the numerical calculation process after the parallelization processing is as shown in fig. 3, wherein the multi-process parallel calculation mode is adopted for the unit point loop and the key loop, so that the numerical calculation speed can be effectively increased, and the calculation result is consistent with the result obtained when the parallel calculation is not adopted. The calculation efficiency can be effectively improved under certain hardware conditions by selecting the proper number of the parallel processes, and the method is wide in applicability.)

1. The parallel cubic lattice integration method of the bond-based near-field dynamics is characterized in that: the method comprises two steps of mechanism modeling and numerical solution. The mechanism modeling means that in the near-field dynamics theory, an analysis object is composed of a large number of material points with physical property information (material performance parameters, positions, displacement and the like), so that the material points can be represented by small cubic lattices with limited number and uniform specification, the small cubic lattices are called point units, the side length is delta x, each point unit represents one material point, and the point units are arranged in parallel to form a structural model of the analysis object;

the numerical solution is to convert the motion equation in the integral form in the basic theory of the bond-based near-field dynamics into a numerical summation mode for calculation on the basis of mechanism modeling, as shown in formula (1),

where t represents time, u represents displacement, n represents the number of time steps, m represents the number of dot cells j or the total number of keys in the near field region of dot cell i, Δ V_jThe volume of a point unit j belonging to the near field region is represented, the acceleration can be represented by referring to the formula (2) by adopting an approximation method, and the acceleration sum speed under a central difference formula is represented by the formula (3).

Similarly, other relevant parameters in the near-field dynamics theoretical model can also be changed into a numerical solution form, such as the denaturation energy density W in the middle of the brittle material and the damage release energy density G in the middle of the brittle material, which are respectively shown in the formula (4) and the formula (5):

thus, the motion equation and related parameters in the model are completely replaced by the simplest four-rule operation, and parameters such as displacement, speed, damage, near field force, deformation energy density of the key, damage release energy density of the key, deformation energy density of the material point, damage release energy density of the material point and the like of each point unit at different moments can be numerically solved through known initial conditions.

Three nested loops are needed to be gone through in the solution of the fraction: 1) time step loop, 2) point unit loop in each time step, 3) all key loops of each point unit;

the parallel numerical calculation method for the cubic lattice integral method mainly aims at the parallel processing of the circular calculation. As can be seen from the analysis of the three loops, in the time step loop, there is a dependency relationship between previous and next time steps, that is, the next time step needs to use the calculation result of the previous time step, and therefore, the loop between the point units and the loop of all keys of each point unit are not parallel to each other, and the calculation between the point units and the calculation of all keys of each point unit are independent from each other, so that the parallelization processing can be performed, and the numerical calculation process after the parallelization processing is as shown in fig. 3, wherein the multi-process parallel calculation mode is adopted for the unit point loop and the key loop, so that the numerical calculation speed can be effectively increased, and the calculation result is consistent with the result obtained when the parallel calculation is not adopted. The calculation efficiency can be effectively improved under certain hardware conditions by selecting the proper number of the parallel processes, and the method is wide in applicability.

Technical Field

The invention relates to the technical field of materials, in particular to a parallel cubic lattice integration method of bond-based near-field dynamics.

Background

The numerical calculation cubic lattice integral method of the bond-based near-field dynamics theoretical model mainly comprises two steps of mechanism modeling and numerical solution. The mechanism modeling means that in the near-field dynamics theory, an analysis object is composed of a large number of material points with physical property information (material performance parameters, positions, displacements and the like), so that the material points can be represented by small cubic lattices with limited number and uniform specifications, the small cubic lattices are called point units, the side length is delta x, each point unit represents one material point, and the point units are arranged in parallel to form a structural model of the analysis object, as shown in fig. 1, the modeling mode does not need to divide a complex grid, and has the advantage of no grid.

The numerical solution is to convert the motion equation in the integral form in the basic theory of the bond-based near-field dynamics into a numerical summation mode for calculation on the basis of mechanism modeling.

In this way, the equation of motion and its related parameters in the model are completely replaced by the simplest four-rule operation, and by using the known initial conditions, the parameters such as displacement, velocity, damage, near field force, deformation energy density of the key, damage release energy density of the key, deformation energy density of the material point, damage release energy density of the material point, and the like of each point unit at different times can be numerically solved, and a cycle body can be used for calculation when the model is solved, as shown in fig. 2.

It can be seen that three nested cycles need to be experienced when solving using the serial cubic lattice integration method: 1) time step loop, 2) point unit loop in each time step, 3) all key loops of each point unit, when the model structure is increased, the calculation amount is exponentially increased along with the model structure.

Disclosure of Invention

The invention aims to provide a parallel cubic lattice integration method of bond-based near-field dynamics, which aims to solve the problem of the mechanical behavior of nonlinear deformation in the background technology.

In order to achieve the purpose, the invention provides the following technical scheme: the parallel cubic lattice integration method of the bond-based near-field dynamics comprises two steps of mechanism modeling and numerical solution. The mechanism modeling means that in the near-field dynamics theory, an analysis object is composed of a large number of material points with physical property information (material performance parameters, positions, displacement and the like), so that the material points can be represented by small cubic lattices with limited number and uniform specification, the small cubic lattices are called point units, the side length is delta x, each point unit represents one material point, and the point units are arranged in parallel to form a structural model of the analysis object;

the numerical solution is to convert the motion equation in the integral form in the basic theory of the bond-based near-field dynamics into a numerical summation mode for calculation on the basis of mechanism modeling, as shown in formula (1),

where t represents time, u represents displacement, n represents the number of time steps, m represents the number of dot cells j or the total number of keys in the near field region of dot cell i, Δ V_jThe volume of a point unit j belonging to the near field region is represented, the acceleration can be represented by referring to the formula (2) by adopting an approximation method, and the acceleration sum speed under a central difference formula is represented by the formula (3).

Similarly, other relevant parameters in the near-field dynamics theoretical model can also be changed into a numerical solution form, such as the denaturation energy density W in the middle of the brittle material and the damage release energy density G in the middle of the brittle material, which are respectively shown in the formula (4) and the formula (5):

thus, the motion equation and related parameters in the model are completely replaced by the simplest four-rule operation, and parameters such as displacement, speed, damage, near field force, deformation energy density of the key, damage release energy density of the key, deformation energy density of the material point, damage release energy density of the material point and the like of each point unit at different moments can be numerically solved through known initial conditions.

Three nested loops are needed to be gone through in the solution of the fraction: 1) time step loop, 2) point unit loop in each time step, 3) all key loops of each point unit;

the parallel numerical calculation method for the cubic lattice integral method mainly aims at the parallel processing of the circular calculation. As can be seen from the analysis of the three loops, in the time step loop, there is a dependency relationship between previous and next time steps, that is, the next time step needs to use the calculation result of the previous time step, and therefore, the loop between the point units and the loop of all keys of each point unit are not parallel to each other, and the calculation between the point units and the calculation of all keys of each point unit are independent from each other, so that the parallelization processing can be performed, and the numerical calculation process after the parallelization processing is as shown in fig. 3, wherein the multi-process parallel calculation mode is adopted for the unit point loop and the key loop, so that the numerical calculation speed can be effectively increased, and the calculation result is consistent with the result obtained when the parallel calculation is not adopted. The calculation efficiency can be effectively improved under certain hardware conditions by selecting the proper number of the parallel processes, and the method is wide in applicability.

Compared with the prior art, the method analyzes and carries out parallel computation design on the multilayer nested loop body in the computation, can effectively improve the computation speed and save the computation time on the premise of not losing the accuracy of the computation result, can select according to the existing hardware condition when selecting the number of parallel processes, and has wider applicability.

Drawings

FIG. 1(a) is a first model diagram of a numerical calculation method;

FIG. 1(b) is a second block diagram of a numerical calculation method;

FIG. 2 is a flow chart of a key-based near-field dynamics numerical computation cubic lattice integral method solution;

FIG. 3 is a flow chart of a bond-based near-field dynamics parallel cubic lattice integration method.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1-3, the present invention provides a technical solution: the numerical calculation cubic lattice integral method of the bond-based near-field dynamics theoretical model mainly comprises two steps of mechanism modeling and numerical solution. The mechanism modeling means that in the near-field dynamics theory, an analysis object is composed of a large number of material points with physical property information (material performance parameters, positions, displacements and the like), so that the material points can be represented by small cubic lattices with limited number and uniform specifications, the small cubic lattices are called point units, the side length is delta x, each point unit represents one material point, and the point units are arranged in parallel to form a structural model of the analysis object, as shown in fig. 1, the modeling mode does not need to divide a complex grid, and has the advantage of no grid.

The numerical solution is to convert the motion equation in the integral form in the basic theory of the bond-based near-field dynamics into a numerical summation mode for calculation on the basis of mechanism modeling, as shown in formula (1),

where t represents time, u represents displacement, n represents the number of time steps, m represents the number of dot cells j or the total number of keys in the near field region of dot cell i, Δ V_jThe volume of a point unit j belonging to the near field region is represented, the acceleration can be represented by referring to the formula (2) by adopting an approximation method, and the acceleration sum speed under a central difference formula is represented by the formula (3).

Similarly, other relevant parameters in the near-field dynamics theoretical model can also be changed into a numerical solution form, such as the denaturation energy density W in the middle of the brittle material and the damage release energy density G in the middle of the brittle material, which are respectively shown in the formula (4) and the formula (5):

in this way, the equation of motion and its related parameters in the model are completely replaced by the simplest four-rule operation, and by using the known initial conditions, the parameters such as displacement, velocity, damage, near field force, deformation energy density of the key, damage release energy density of the key, deformation energy density of the material point, damage release energy density of the material point, and the like of each point unit at different times can be numerically solved, and a cycle body can be used for calculation when the model is solved, as shown in fig. 2.

It can be seen that three nested cycles need to be experienced when solving using the serial cubic lattice integration method: 1) time step circulation, 2) point unit circulation in each time step, and 3) all key circulation of each point unit, wherein when the model structure is increased, the calculated amount is exponentially increased, and therefore, a parallel numerical calculation method aiming at a cubic lattice integration method is designed, and parallel processing is mainly carried out aiming at circulation calculation. As can be seen from the analysis of the three loops, in the time step loop, there is a dependency relationship between previous and next time steps, that is, the next time step needs to use the calculation result of the previous time step, and therefore, the loop between the point units and the loop of all keys of each point unit are not parallel to each other, and the calculation between the point units and the calculation of all keys of each point unit are independent from each other, so that the parallelization processing can be performed, and the numerical calculation process after the parallelization processing is as shown in fig. 3, wherein the multi-process parallel calculation mode is adopted for the unit point loop and the key loop, so that the numerical calculation speed can be effectively increased, and the calculation result is consistent with the result obtained when the parallel calculation is not adopted. The calculation efficiency can be effectively improved under certain hardware conditions by selecting the proper number of the parallel processes, and the method is wide in applicability.

When the cubic lattice integration method is used for carrying out numerical calculation solving on the key-based near-field dynamics model, the calculation amount is exponentially multiplied along with the increase of the model, so that the analysis and parallel calculation design are carried out on the multilayer nested loop body in the calculation, the calculation speed can be effectively improved on the premise of not losing the accuracy of the calculation result, the calculation time is saved, and in addition, when the number of parallel processes is selected, the selection can be carried out according to the existing hardware condition, so that the method has wider applicability.

The embodiment mainly comprises two calculation ideas, namely a calculation idea of using a multilayer circulation body to calculate each parameter of a crystal lattice, and a parallel algorithm design idea of using a multilayer circulation nested body in a serial numerical calculation method.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.